https://neckpinch.com/authors/jeffrey-streets/New arXiv papers by Jeffrey Streets, from Neckpinch Tue, 03 Nov 2026 07:15:30 GMT https://arxiv.org/abs/2608.25829arxiv:2608.25829Wed, 26 Aug 2026 00:00:00 GMTJeffrey Streets — Adapting ideas of, we show that compact generalized Ricci solitons (GRS) have positive Yamabe invariant. We observe a Cheeger-Gromoll-type splitting theorem for GRS as a corollary of the splitting theorem for Bakry-Émery Ricci curvature in. Using this we show that low dimensional GRS are diffeomorphic to S³ / Γ or S³ × S¹ / Γ. We determine various topological constraints on string backgrounds (Bismut-Hermitian-Einstein (BHE), strong torsion G₂, strong torsion Spin(7)-manifolds) and show in most cases that they cannot exist on the same manifolds as their classical special holonomy counterparts. Finally we determine the topology of BHE threefolds under natural constraints, relying on an extension of parts of Kollar's characterization of Seifert fibered 5-manifolds over complex orbifolds.Generalized & G₂ flowsRicci solitonsRicci-flat & Calabi–Yau3-manifoldsLimit spaces & RCD https://arxiv.org/abs/2608.14358arxiv:2608.14358Fri, 14 Aug 2026 00:00:00 GMTBeatrice Brienza, Jeffrey Streets — We identify a Hermitian curvature flow which preserves HKT geometry, and whose fixed points are HKT-Einstein metrics, equivalent to a flow suggested by Verbitsky in the context of the quaternionic Monge-Ampère equation. We exhibit a fundamental regularity obstruction and a monotonicity formula for the Chern scalar curvature. We formulate a maximal existence time conjecture for this flow, and give a conditional resolution. We establish the existence conjecture in dimension four. We show the existence of a divergent sequence of HKT-Einstein metrics on quaternionic Hopf surfaces. These are the first non-homogeneous examples in the literature, and indicate the delicacy of the convergence question. Finally we classify which strong HKT structures arising from bi-invariant metrics on Lie groups are also HKT-Einstein.Generalized & G₂ flowsEinstein metrics4-manifoldsKähler geometryScalar curvatureHomogeneous spaces https://arxiv.org/abs/2512.11246arxiv:2512.11246Fri, 12 Dec 2025 00:00:00 GMTJeffrey Streets, Xiaokang Wang — We establish global existence of the pluriclosed flow with arbitrary initial data on Oeljeklaus-Toma manifolds, and Gromov-Hausdorff convergence of blowdown limits to a torus under natural conjectural bounds on the flow at infinity. In the case of generalized Kähler-Ricci flow we prove refined a priori estimates in support of these conjectural bounds.Ricci flowKähler–Ricci flowGeneralized & G₂ flowsKähler geometryLimit spaces & RCDLong-time existence & convergence https://arxiv.org/abs/2511.20773arxiv:2511.20773Tue, 25 Nov 2025 00:00:00 GMTAaron Kennon, Jeffrey Streets — String backgrounds, defined here as metric connections with skew-symmetric torsion and reduced holonomy, yield generalized Ricci solitons relative to the Lee vector field. By a variational argument using the string action, they are also gradient generalized Ricci solitons relative to a potential function. These two observations combine to yield a canonical symmetry, and in this work we derive fundamental features of the transverse geometry, and rigidity phenomena. We prove in a unified conceptual fashion that the transverse geometry satisfies the string generalized Ricci soliton equations (a simplified Hull-Strominger system) in many settings including almost Hermitian, almost contact, SU(3), G₂, and Spin(7) geometry. We also show that the transverse geometry is always conformally co-closed, with the conformal factor given by the associated soliton potential.Generalized & G₂ flowsRicci solitonsStability & uniquenessSasakian & contact geometry https://arxiv.org/abs/2509.01639arxiv:2509.01639Mon, 01 Sep 2025 00:00:00 GMTVestislav Apostolov, Giuseppe Barbaro, Jeffrey Streets, Yury Ustinovskiy — We establish a local equivalence between toric steady Kähler-Ricci solitons and A-type toric generalized Kähler-Ricci solitons (GKRS). Under natural global conditions we show this equivalence extends to complete GKRS, yielding a general construction of new examples in all dimensions. We show that in four dimensions, all GKRS are either described by the generalized Kähler Gibbons-Hawking ansatz, or have split tangent bundle, or are A-type toric. This yields a local classification in four dimensions, together with a conjecturally exhaustive construction of complete symplectic-type examples.Ricci solitonsKähler–Ricci solitonsKähler geometry https://arxiv.org/abs/2408.11674arxiv:2408.11674Wed, 21 Aug 2024 00:00:00 GMTMario Garcia-Fernandez, Raul Gonzalez Molina, Jeffrey Streets — We define a natural extension of pluriclosed flow aiming at constructing solutions of the Hull-Strominger system. We give several geometric formulations of this flow, which yield a series of a priori estimates for the flow and also for the Hull-Strominger system. The evolution equations are derived using the theory of string algebroids, a class of Courant algebroids which occur naturally in higher gauge theory. Using this, we interpret the flow as generalized Ricci flow and also as a higher/coupled version of Hermitian-Yang-Mills flow, proving furthermore that it is compatible with symmetry reduction. Regarding our main analytical results, we prove a priori C^(∞) estimates for uniformly parabolic solutions. This in particular settles the question of smooth regularity of uniformly elliptic solutions of the Hull-Strominger system, generalizing Yau's C³ estimate for the complex Monge-Ampère equation. We prove global existence and convergence results for the flow on special backgrounds, and discuss a conjectural relationship of the flow to the geometrization of Reid's fantasy.Ricci flowGeneralized & G₂ flowsGeometrizationKähler geometryLong-time existence & convergence https://arxiv.org/abs/2404.14595arxiv:2404.14595Mon, 22 Apr 2024 00:00:00 GMTVestislav Apostolov, Jeffrey Streets, Yury Ustinovskiy — Building on works of Boulanger and Goto, we show that Goto's scalar curvature is the moment map for an action of generalized Hamiltonian automorphisms of the associated Courant algebroid, constrained by the choice of an adapted volume form. We derive an explicit formula for Goto's scalar curvature, and show that it is constant for generalized Kähler-Ricci solitons. Restricting to the generically symplectic type case, we realize the generalized Kähler class as the complexified orbit of the Hamiltonian action above. This leads to a natural extension of Mabuchi's metric and K-energy, implying a conditional uniqueness result. Finally, in this setting we derive a Calabi-Matsushima-Lichnerowicz obstruction and a Futaki invariant.Ricci solitonsKähler–Ricci solitonsKähler geometryScalar curvatureStability & uniquenessKähler–Einstein & K-stability https://arxiv.org/abs/2402.11069arxiv:2402.11069Fri, 16 Feb 2024 00:00:00 GMTJeffrey Streets, Charles Strickland-Constable, Fridrich Valach — We develop a theory of Ricci flow for metrics on Courant algebroids which unifies and extends the analytic theory of various geometric flows, yielding a general tool for constructing solutions to supergravity equations. We prove short time existence and uniqueness of solutions on compact manifolds, in turn showing that the Courant isometry group is preserved by the flow. We show a scalar curvature monotonicity formula and prove that generalized Ricci flow is a gradient flow, extending fundamental works of Hamilton and Perelman. Using these we show a convergence result for certain nonsingular solutions to generalized Ricci flow.Ricci flowGeneralized & G₂ flowsScalar curvatureStability & uniquenessHarmonic maps & DeTurck trickPhysics https://arxiv.org/abs/2306.01649arxiv:2306.01649Fri, 02 Jun 2023 00:00:00 GMTEva Kopfer, Jeffrey Streets — We prove results relating the theory of optimal transport and generalized Ricci flow. We define an adapted cost functional for measures using a solution of the associated dilaton flow. This determines a formal notion of geodesics in the space of measures, and we show geodesic convexity of an associated entropy functional. Finally, we show monotonicity of the cost along the backwards heat flow, and use this to give a new proof of the monotonicity of the energy functional along generalized Ricci flow.Ricci flowGeneralized & G₂ flowsLimit spaces & RCD https://arxiv.org/abs/2211.09104arxiv:2211.09104Wed, 16 Nov 2022 00:00:00 GMTVestislav Apostolov, Xin Fu, Jeffrey Streets, Yury Ustinovskiy — We formulate an extension of the Calabi conjecture to the setting of generalized Kähler geometry. We show a transgression formula for the Bismut Ricci curvature in this setting, which requires a new local Goto/Kodaira-Spencer deformation result, and use it to show that solutions of the generalized Calabi-Yau equation on compact manifolds are classically Kähler, Calabi-Yau, and furthermore unique in their generalized Kähler class. We show that the generalized Kähler-Ricci flow is naturally adapted to this conjecture, and exhibit a number of a priori estimates and monotonicity formulas which suggest global existence and convergence. For initial data in the generalized Kähler class of a Kähler Calabi-Yau structure we prove the flow exists globally and converges to this unique fixed point. This has applications to understanding the space of generalized Kähler structures, and as a special case yields the topological structure of natural classes of Hamiltonian symplectomorphisms on hyperKähler manifolds. In the case of commuting-type generalized Kähler structures we establish global existence and convergence with arbitrary initial data to a Kähler, Calabi-Yau metric, which yields a new d d^c-lemma for these structures.Ricci flowKähler–Ricci flowGeneralized & G₂ flowsRicci-flat & Calabi–YauKähler geometryLong-time existence & convergence https://arxiv.org/abs/2207.13197arxiv:2207.13197Tue, 26 Jul 2022 00:00:00 GMTJeffrey Streets — We derive a family of weighted scalar curvature monotonicity formulas for generalized Ricci flow, involving an auxiliary dilaton field evolving by a certain reaction-diffusion equation motivated by renormalization group flow. These scalar curvature monotonicities are dual to a new family of Perelman-type energy and entropy monotonicity formulas by coupling to a solution of the associated weighted conjugate heat equation. In the setting of Ricci flow, we further obtain a new family of convex Nash entropies and pseudolocality principles.Ricci flowGeneralized & G₂ flowsHeat kernelScalar curvaturePhysics https://arxiv.org/abs/2207.05633arxiv:2207.05633Tue, 12 Jul 2022 00:00:00 GMTEva Kopfer, Jeffrey Streets — As a consequence of the Bochner formula for the Bismut connection acting on gradients, we show sharp universal Poincaré and log-Sobolev inequalities along solutions to generalized Ricci flow. Using the two-form potential we define a twisted connection on spacetime which determines an adapted Brownian motion on the frame bundle, yielding an adapted Malliavin gradient on path space. We show a Bochner formula for this operator, leading to characterizations of generalized Ricci flow in terms of universal Poincaré and log-Sobolev type inequalities for the associated Malliavin gradient and Ornstein-Uhlenbeck operator.Ricci flowGeneralized & G₂ flowsPerelman entropy https://arxiv.org/abs/2202.04564arxiv:2202.04564Wed, 09 Feb 2022 00:00:00 GMTJeffrey Streets, Gang Tian — Using dynamical stability of symplectic curvature flow, we show that on a compact Calabi-Yau manifold, any small symplectic deformation of a Kähler form remains Kähler.Other curvature flowsRicci-flat & Calabi–YauKähler geometryStability & uniqueness https://arxiv.org/abs/2109.10295arxiv:2109.10295Tue, 21 Sep 2021 00:00:00 GMTVestislav Apostolov, Jeffrey Streets, Yury Ustinovskiy — Under broad hypotheses we derive a scalar reduction of the generalized Kähler-Ricci soliton system. We realize solutions as critical points of a functional analogous to the classical Aubin energy defined on the orbit of a natural Hamiltonian action of diffeomorphisms, thought of as a generalized Kähler class. This functional is convex on a large set of paths in this space, and using this we show rigidity of solitons in their generalized Kähler class. As an application we prove uniqueness of the generalized Kähler-Ricci solitons on Hopf surfaces constructed in arXiv:1907.03819, finishing the classification in complex dimension 2.Ricci solitonsKähler–Ricci solitonsKähler geometryStability & uniqueness https://arxiv.org/abs/2109.07562arxiv:2109.07562Wed, 15 Sep 2021 00:00:00 GMTSteven Gindi, Jeffrey Streets — We study solutions to generalized Ricci flow on four-manifolds with a nilpotent, codimension 1 symmetry. We show that all such flows are immortal, and satisfy type III curvature and diameter estimates. Using a new kind of monotone energy adapted to this setting, we show that blowdown limits lie in a canonical finite-dimensional family of solutions. The results are new for Ricci flow.Ricci flowGeneralized & G₂ flows4-manifoldsHomogeneous spacesLong-time existence & convergence