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Ricci flow papers from 2025
270 papers from 2025, out of 1,462 papers on Ricci flow, Ricci solitons, Perelman's methods and the Poincaré conjecture, plus the geometric flows that share their tools — mean curvature flow, curve shortening, Yamabe flow — marked Wider flows. 13 of them are from the last seven days. Click a title for the PDF, or the arXiv number for the abstract.
Archive
All 270 papers from 2025
Topic
December 2025 21
Classification of ancient cylindrical mean curvature flows and the Mean Convex Neighborhood Conjecture
Rotationally symmetric translating solitons of fully nonlinear extrinsic geometric flows: Classification and Applications
Fano Fibrations and Twisted Kähler-Einstein Metrics II: The Kähler-Ricci Flow
Fano Fibrations and Twisted Kähler-Einstein Metrics I
Local well-posedness of the skew mean curvature flow for large data
A Spinorial Heat Flow Framework for Geometric Degeneration on -Manifolds
Locally constrained inverse curvature flow and Alexandrov-Fenchel type inequalities in de Sitter space
An Aubin continuity path for asymptotically conical toric shrinking gradient Kähler-Ricci solitons: openness and a solution for
Characterizations of Almost Ricci Bourguignon Solitons
Parabolic free boundary phase transition and mean curvature flow
Rigidity of weighted manifolds via classification results for semilinear equations
Pluriclosed flow on Oeljeklaus-Toma manifolds
Curvature estimates for steady and expanding solitons in higher dimensions
Geometric properties of second Ricci solitons
Mean curvature flow near a peanut solution
Existence of twisted Calabi flow and deformation from the -flow to Calabi flow
K-polystability of Asymptotically Conical Kähler-Ricci Shrinkers
Self-Expanding Solutions to the Mean Curvature Flow for Multiphase Surfaces with Regular Junctions
Twisted Calabi functional and twisted Calabi flow
A Dynamical Approach to the Berezin-Li-Yau Inequality
November 2025 18
Harnack Inequality for -Mean Curvature Flow
Monotonicity of Perelman -Entropy of Mean Curvature Flow
Classification of Minimal Surfaces and Solitons to the Mean Curvature Flow in as Translation Surfaces
Flows of conformally coclosed -structures with dilaton
The canonical symmetry reduction of string backgrounds
Linear stability and instability of Kähler Ricci solitons
Decay order bound for mean curvature flow near compact singularities
Weak transcendental base-point freeness and diameter lower bounds for the Kähler-Ricci flow
Kähler-Ricci flows coming out of metric spaces
Quasi-Einstein Metrics and a curvature identity associated with the Ricci flow
Synthetic approaches to Ricci flows
Dynamical functionals on ancient ARF Ricci flows
Ricci solitons of special Lorentzian Lie groups with a four-dimensional isometry group
Monotonicity of topological entropy along the Ricci flow near a hyperbolic metric
Rigidity of Gradient Shrinking Ricci Solitons with a Vanishing Bach-like Tensor and Related Variational Formulas
Topologically Stabilized Torsion in Weak-Field Gravity: A Ricci-Flow Framework
Minimal Degrees, Volume Growth, and Curvature Decay on Complete Kähler Manifolds
Stability of volume and area preserving mean curvature flow in asymptotic Schwarzschild space
October 2025 41
Singular sets in noncollapsed Ricci flow limit spaces
The Cauchy problem for gradient generalized Ricci solitons on a bundle gerbe
The -th dual Minkowski problem for the -torsional rigidity corresponding to a -Hessian equation
Ricci flow and the scalar curvature rigidity of Einstein manifolds
On the rate of convergence of cylindrical singularity in mean curvature flow
Mean curvature flow into an ambient Riemannian manifold evolving by Ricci flow coupled with harmonic map heat flow
Higher-dimensional flying wing Steady Ricci Solitons
Singularities of the Lagrangian mean curvature flow at the critical Lagrangian phase
curvature bounds for Type I Ricci flows
Anisotropic mean curvature flow with contact angle and Neumann boundary conditions in arbitrary dimensions
Two dimensional anisotropic mean curvature flow with contact angle condition
Ricci Flow on ALF manifolds
Strong uniqueness of tangent flows at cylindrical singularities in Ricci flow
The Bounded Diameter Conjecture and Sharp Geometric Estimates for Mean Curvature Flow
Equivalence of weak solution concepts for mean curvature flow
Cohomogeneity One Expanding Ricci Solitons and the Expander Degree
Singularities of Curve Shortening Flow with Convex Projections
Calabi flow with bounded scalar curvature (II)
Almost Gradient Ricci Solitons on Static Spacetime
Diameter bounds in 3d Type I Ricci flows
Moving Manifolds and the Poincare Conjecture
Local structure of gradient almost Ricci solitons with harmonic Weyl tensor
Geometric study of non-constant vector fields making hyperbolic space Ricci-Bourguignon solitons
Complete gradient Einstein-type Sasakian manifolds with
On the structure of noncollapsed Ricci flow limit spaces
Local umbilic, convexity and cylindrical estimates for fully nonlinear curvature flows
The Ricci tensor of a gradient Ricci soliton with harmonic Weyl tensor
Mean curvature flow converging to an minimizing cone and its Hardt-Simon foliation
Is a complete Riemannian manifold with positively pinched Ricci curvature compact
Existence of martingale solutions for a stochastic weighted mean curvature flow of graphs
Positive Hermitian curvature flow on 2-step nilpotent Lie groups
Asymptotic behaviour of the weak inverse anisotropic mean curvature flow
Non-uniqueness in Mean Curvature Flow: Non-canonical solutions via the parabolic Allen–Cahn
Stability of asymptotically conical gradient Kähler-Ricci expanders
On the Bergman metric of Cartan-Hartogs domains
On curvature estimates for four-dimensional gradient Ricci solitons
Ancient Gauss Curvature Flows of Bounded Width
Curvature pinching of asymptotically conical gradient expanding Ricci solitons
Inverse curvature flow of closed Legendre curves
Mean curvature flow through singularities
Approximate mean curvature flows of a general varifold, and their limit spacetime Brakke flow
September 2025 30
An Ancient Stacked Pancake Solution to Mean Curvature Flow
A Characterization of Quasi-Einstein Metrics
Steady Gradient Ricci Solitons with Symmetry
Legendrian curve flow in Sasakian sub-Riemannian 3-manifolds
Two Comments on "Laplace comparison on Kahler Ricci flow and convergence (arXiv:2509.14820v1)"
An ancient Ricci flow emerging from Taub-Bolt
Towards a Taub-Bolt to Taub-NUT via Ricci flow with surgery
Neural Feature Geometry Evolves as Discrete Ricci Flow
On the Ricci flow on Trees
Noncollapsing for Curvature Flows with Inhomogeneous Speeds
Gradient Shrinking Ricci Solitons and Modified Sectional Curvature
Ricci Flow on Weighted Digraphs with Balancing Factor
Existence of flat flows for volume-preserving mean curvature flow with contact angle
Curvature tensors and hyperbolic solitons on Lorentzian trans-Sasakian space form
On the geometry and uniqueness of asymptotically locally hyperbolic static vacuum black holes
Well-posedness of Ricci Flow in Lorentzian Spacetime and its Entropy Formula
Huisken's Distance Comparison Principle in Higher Codimension
Laplace comparison on Kähler Ricci flow and convergence
An -Regularity Theorem for Non-collapsed Ricci Flow
On Shrinking Ricci solitons with positive isotropic curvature in higher dimensions
Sigma model renormalisation group flows, singularities and some remarks on cosmology
Uniqueness of tangent planes and (non-)removable singularities at infinity for collapsed translators
On the avoidance principle for codimension 1 space-time Brakke flows
Integral Brakke approximate equality for an approximate mean curvature flow
Curvature Flow of Networks with Triple Junction Drag
A note on a diffeomorphism criterion via long-time Ricci flow
Linear stability of the blowdown Ricci shrinker in 4D
Regularity of cylindrical singular sets of mean curvature flow
Toric geometry of generalized Kähler-Ricci solitons
Gradient Shrinking Sasaki-Ricci Solitons with Harmonic Weyl Tensor
August 2025 23
Convexity of mean convex asymptotically conical self-expanders to the mean curvature flow
Minimal surface entropy and applications of Ricci flow on finite-volume hyperbolic 3-manifolds
On the stability of Ricci flow on hyperbolic 3-manifolds of finite volume
Invariant -translators for the Gauss curvature flow in Euclidean space
Contractive transport maps from to nearly spherical surfaces with positive Ricci curvature
Green's function estimates for compact Kähler manifolds and applications
Geometry and Topology of Gradient Shrinking Sasaki-Ricci Solitons
Almost Ricci Solitons on Class Hypersurfaces of Product Spaces
BRIDGES Lectures: Flows of geometric structures, especially -structures
Geometric Structure of Ends of Ricci Shrinkers
The fundamental physical importance of generic off-diagonal solutions and Grigori Perelman entropy in the Einstein gravity theory
Ricci Solitons on a family of three dimensional Lorentzian Walker manifolds
An alternative solvability criterion for the Dirichlet problem for the minimal surface equation and an application to the mean curvature flow
Weighted, Multiphase, Volume-Preserving Mean Curvature Flow as Limit of the MBO Scheme on Manifolds
Characterizations of weak almost -manifolds with curvature properties
Rigidity theorems for complete Legendrian self-shrinkers
Refined behavior description of the normalized Ricci flow on homogeneous spaces
Long time behavior of a class of non-homogeneous anisotropic fully nonlinear curvature flows
On a general class of free boundary Monge-Ampère equations
Cylindrical tangent flows in mean curvature flow
A variational approach to the volume-preserving anisotropic mean curvature flow in 2D
Core detection via Ricci curvature flows on weighted graphs
Shrinkers of the area-preserving curve-shortening flow: Existence and saddle-point property
July 2025 24
Einstein metrics and Killing spinors on pseudo-Riemannian solvmanifolds
Universal embeddings of flag manifolds and rigidity phenomena
On an area-preserving inverse curvature flow for plane curves
Convergence of the fractional Yamabe flow for arbitrary initial energy
Self-expanders of positive genus
Discrete conformal structures on surfaces with boundary (III) – Deformation
The dynamical Alekseevskii conjecture in dimension five
Backwards uniqueness for Mean curvature flow with asymptotically conical singularities
Asymptotic behavior at infinity and existence of solutions to the Lagrangian mean curvature flow in
Rigidity of solitons of the Gauss curvature flow in Euclidean space
Hamilton's identity and rigidity of complete gradient solitons
The existence and uniqueness of infinite combinatorial Yamabe flows
Inverse curvature flows for capillary hypersurfaces in the unit ball
A curvature flow approach to dorsal closure modelling
A locally constrained inverse Hessian quotient flow in de Sitter space
Short-time existence of Lagrangian mean curvature flow
Generalized Ricci solitons on LP-Sasakian manifolds admitting the general connection
Varifold solutions to Volume-Preserving Mean Curvature Flow: existence and weak-strong uniqueness
Generic mean curvature flow with obstacles
Finite extinction time of a family of homogeneous Ricci flows
On a parabolic curvature lower bound generalizing Ricci flows
Extensions and Applications of Bredon's Trick in Geometric and Topological Contexts
Improved explicit estimates for the discrete Laplace operator with hyperbolic circle patterns
When can minimal hypersurfaces be connected by mean curvature flow?
June 2025 13
The Dirichlet problem for the minimal surface system on smooth domains
New weighted Alexandrov-Fenchel type inequalities and Minkowski inequalities in space forms
On Sun-Zhang's theory of Fano fibrations – weighted volumes, moduli and bubbling Fano fibrations
Expanding Ricci solitons and Higgs bundles
The capillary Gauss curvature flow
--Ricci solitons on weak Kenmotsu -manifolds
Combinatorial p-th Calabi flow for finite and infinite ideal circle patterns
Variational Nonlinear and Nonlocal Curvature Flows
Elementary discrete diffusion/redistancing schemes for the mean curvature flow
Characterization of Infinite Ideal Polyhedra in Hyperbolic 3-Space via Combinatorial Ricci Flow
Gradient estimates and parabolic frequency monotonicity for positive solutions of the heat equation under generalized Ricci flow
On Ricci Solitons with Isoparametric Potential Functions
Rigidity of Five-Dimensional shrinking gradient Ricci solitons
May 2025 23
Branched -combinatorial Ricci flows on closed surfaces with Euler characteristic
The Minkowski problem for the -torsional rigidity
Brakke inequality and the existence of Brakke-flow for volume preserving mean curvature flow
Rotationally symmetric Ricci Flow on
Second boundary value problem for the Hessian curvature flow
On dual regime in Yang-Baxter deformed sigma models
On steady and expanding Ricci solitons with asymptotic symmetries
A two-player zero-sum probabilistic game that approximates the mean curvature flow
A prescribed curvature flow on hyperbolic surfaces with infinite topological type
The mean curvature flow of subgroups on Lie groups of dimension three
Existence proofs for rotationally symmetric translating solutions to mean curvature flow
Finite generation of the ring of holomorphic functions with polynomial growth on the Kähler-Ricci shrinker
Mean Curvature Flow of Closed Curves Evolving in Two Dimensional Manifolds
An Intersection Principle for Mean Curvature Flow
A -Hilbert functional in -geometry
Infinite combinatorial Ricci flow in spherical background geometry
Global well-posedness in the critical Besov space of the skew mean curvature flow in
An eigenvalue estimate for self-shrinkers in a Ricci shirinker
On Perelman's -entropy and Shannon entropy power for super Ricci flows on metric measure spaces
Ricci Solitons on the Poincaré upper half plane
Correction to: Curvature growth of some 4-dimensional gradient Ricci soliton singularity models
Remarks on Singular Kähler-Einstein Metrics
On the geometry of Riemannian warped product maps
April 2025 20
Uniqueness of asymptotically conical Kähler-Ricci flow
Planarity and convexity for pinched ancient solutions of mean curvature flow
Local Existence Of The Symplectic Gradient Flow On The Hyperkähler Four-dimensional Flat Torus
Mean Curvature Flow for Isoparametric Submanifolds in Hyperbolic Spaces
Resolving the S8 tension with the Lambda Prime () model
Rigidity of positively curved Steady gradient Ricci solitons on orbifolds
Dynamical stability of Pluriclosed and Generalized Ricci solitons
Prescribing hyperbolic bordered surfaces via combinatorial flows
Volume estimates for the singular sets of mean curvature flows
Rigidity of ancient ovals in higher dimensional mean curvature flow
Chern-Ricci flow and t-Gauduchon Ricci-flat condition
Generalized circle patterns on surfaces with cusps
Gap Theorem on locally conformally flat manifold
Monotonicity of the Liouville entropy along the Ricci flow on surfaces
On the tangent flow to the collapsing Kähler-Ricci flow on Hirzebruch surfaces
A distributional approach to nonlocal curvature flows
Combinatorial Ricci flows on infinite disk triangulations
Remarks on minimal hypersurfaces in shrinking gradient Ricci solitons
Convergence of Ricci flow and long-time existence of Harmonic map heat flow
A game approach to free boundary problems of anisotropic forced mean curvature flow equations
March 2025 21
Lagrangian mean curvature flow of surfaces with mean curvature bound
Convergence of thresholding energies for anisotropic mean curvature flow on inhomogeneous obstacle
Uniqueness of Ricci flow with scaling invariant estimates
Diffusion-aggregation equations and volume-preserving mean curvature flows
Geometric Meta-Learning via Coupled Ricci Flow: Unifying Knowledge Representation and Quantum Entanglement
Classification of gradient Einstein-type Kähler manifolds with
--Ricci solitons and Einstein metrics on a weak -Kenmotsu manifold
Hermitian metrics on complex non-Kähler manifolds
Upper bounds for the Alexandrov-Fenchel deficit via integral formulas
Cohomogeneity one 4-dimensional gradient Ricci solitons
On the weakly conical expanding gradient Ricci solitons
Infinite-dimensional dynamical instabilities of noncompact stationary Ricci flow solutions
How close is too close for singular mean curvature flows?
Differential topology of the spaces of asymptotically stable vector fields and Lyapunov functions
Hyperbolization and geometric decomposition of a class of 3-manifolds
Ricci flow from singular spaces with bounded curvature
The asymptotic of the Mullins-Sekerka and the area-preserving curvature flow in the planar flat torus
Shrinking gradient Kähler-Ricci solitons are simply-connected
Perelman's entropy and heat kernel bounds on RCD spaces
Mean curvature flow for principal orbits of Hermann actions on rank two symmetric spaces
A gap Theorem on closed self-shrinkers of mean curvature flow
February 2025 20
Generating Shrinkers by Mean Curvature Flow
Non-collapsed finite time singularities of the Ricci flow on compact Kähler surfaces are of Type I
Existence of Constant Mean Curvature Surfaces in Asymptotically Flat and Asymptotically Hyperbolic Manifolds
A delayed interior area-to-height estimate for the Curve Shortening Flow
On a non-local area-preserving curve flow
Transverse Rigidity of Shrinking Sasaki-Ricci Solitons
An -regularity theorem for Perelman's reduced volume
Uniqueness of asymptotically conical shrinking gradient Kähler-Ricci solitons
Higher-Dimensional Vacuum Einstein Equations: Symmetry, New Solutions, and Ricci Solitons
On Kähler-Einstein Currents
3-Manifolds with positive scalar curvature and bounded geometry
On mean curvature flow solitons in the sphere
Local singularities of compact multiply warped Ricci flow solutions
Generalized Harnack Inequality for Mean Curvature Flow and Ancient Solutions
Combinatorial Ricci Flow and Thurston's Triangulation Conjecture
Some remarks on strong -structures with torsion
Geometric flows and space-periodic solitons on the light-cone
Quantitative uniqueness for mean curvature flow
Courant Algebroid Relations, T-Dualities and Generalised Ricci Flow
A normalized Ricci flow on surfaces with boundary towards the complete hyperbolic metric
January 2025 16
Passing through nondegenerate singularities in mean curvature flows
Volume preserving mean curvature flow of round surfaces in asymptotically flat spaces
Deriving Perelman's entropy from Colding's monotonic volume
Long-time behavior of Ricci flow on some complex surfaces
Quaternionic Kähler manifolds fibered by solvsolitons
Threshold dynamics approximation schemes for anisotropic mean curvature flows with a forcing term
3-symmetric spaces, Ricci solitons, and homogeneous structures
Synthetic notions of Ricci flow for metric measure spaces
Rigidity Results Involving Stabilized Scalar Curvature
Singularities of mean curvature flow with bounded mean curvature and Morse index
Drift-harmonic functions with polynomial growth on asymptotically paraboloidal manifolds
Prescribed Chern scalar curvature flow on compact Hermitian manifolds with negative Gauduchon degree
Existence of weak solutions to volume-preserving mean curvature flow with obstacles
Combinatorial Calabi flow for ideal circle pattern
Combinatorial Calabi flows with ideal circle patterns
The Impact of Socio-Economic Challenges and Technological Progress on Economic Inequality: An Estimation with the Perelman Model and Ricci Flow Methods
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