Paper · Nov 4, 2026

Uniqueness of Ricci flows from singular initial data

Laura Flower, Man-Chun Lee, Felix Schulze

math.DGarXiv:2611.06814
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Abstract

We establish uniqueness of Ricci flows with non-negative sectional curvatures and scaling invariant curvature bounds, assuming that the induced distance functions converge to the same initial distance function up to isometry. In the compact case, restricting the size of the initial singular set, we also establish uniqueness under suitable weaker conditions.

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Submitted
Nov 4, 2026
Subjects
math.DG, math.AP

Comments: 30 pages, comments welcome!

Ricci flowWeak & singular flowsStability & uniqueness

Its neighbourhood

Connected papers

The 8 papers on this site closest to this one, judged by the topics they share, the words and phrases in their titles and abstracts, and their authors. They are not its citations, but a map of the work around it. Papers here go back to 2021, plus the canon.

Connected papers This paper in the centre and the 8 papers closest to it around it, in date order clockwise from the top. The closer a paper sits to the centre, the stronger the connection. This paper Initial stability estimates for Ricci flow and three dimensional Ricci-pinched manifolds (Alix Deruelle, Felix Schulze and Miles Simon, 2022)2Deruelle 2022 Rigidity of Lipschitz map using harmonic map heat flow (Man-Chun Lee and Luen-Fai Tam, 2022)3Lee 2022 Expanding Ricci solitons coming out of weakly PIC1 metric cones (Pak-Yeung Chan, Man-Chun Lee and Luke T. Peachey, 2024)7Chan 2024 Ricci-DeTurck Flow from Initial Metric with Morrey-type Integrability Condition (Man-Chun Lee and Stephen Shang Yi Liu, 2024)4Lee 2024 Preserving curvature lower bounds when Ricci flowing non-smooth initial data (Miles Simon, 2024)8Simon 2024 Uniqueness of Ricci flow with scaling invariant estimates (Man-Chun Lee, 2025)5Lee 2025 PIC1 pinched manifolds are flat or compact (Alix Deruelle, Man-Chun Lee, Felix Schulze et al., 2026)6Deruelle 2026 On the uniqueness of Ricci flows from certain Alexandrov spaces (Laura Flower, 2026)1Flower 2026
Closer to the centre: more closely connected. Clockwise from the top: oldest to newest. Ricci flowWider flowsalso connected to each other
  1. On the uniqueness of Ricci flows from certain Alexandrov spaces

    Laura Flower

    Topics Weak & singular flows, Stability & uniqueness · Same author Laura Flower · Shared terms “singular initial”, “initial data”, “scaling invariant”

  2. Initial stability estimates for Ricci flow and three dimensional Ricci-pinched manifolds

    Alix Deruelle, Felix Schulze and Miles Simon

    Topics Weak & singular flows, Stability & uniqueness · Same author Felix Schulze

  3. Rigidity of Lipschitz map using harmonic map heat flow

    Man-Chun Lee and Luen-Fai Tam

    Topics Weak & singular flows, Stability & uniqueness · Same author Man-Chun Lee · Shared terms “initial data”, “isometry”

  4. Ricci-DeTurck Flow from Initial Metric with Morrey-type Integrability Condition

    Man-Chun Lee and Stephen Shang Yi Liu

    Topics Weak & singular flows, Stability & uniqueness · Same author Man-Chun Lee · Shared terms “singular set”

  5. Uniqueness of Ricci flow with scaling invariant estimates

    Man-Chun Lee

    Topics Stability & uniqueness · Same author Man-Chun Lee · Shared terms “scaling invariant”, “invariant curvature”, “curvature bounds”

  6. PIC1 pinched manifolds are flat or compact

    Alix Deruelle, Man-Chun Lee, Felix Schulze et al.

    Topics Ricci flow · Same authors Man-Chun Lee, Felix Schulze

  7. Expanding Ricci solitons coming out of weakly PIC1 metric cones

    Pak-Yeung Chan, Man-Chun Lee and Luke T. Peachey

    Topics Weak & singular flows · Same author Man-Chun Lee

  8. Preserving curvature lower bounds when Ricci flowing non-smooth initial data

    Miles Simon

    Topics Weak & singular flows · Shared terms “initial data”

Read around it

Background reading

The guides for the topics of this paper: what each idea is, why it matters, and the papers to read first.

Ricci flow Hamilton's Ricci flow evolves a Riemannian metric by minus twice its Ricci curvature. It is a nonlinear heat equation for geometry: it spreads… Start with: Three-manifolds with positive Ricci curvature (Hamilton, 1982) Weak & singular flows Running a flow when the data isn't smooth or singularities form: Ricci flows from rough initial data, through singularities and on metric measure… Start with: Deformation of C⁰ Riemannian metrics in the direction of their Ricci curvature (Simon, 2002) Stability & uniqueness When does a flow started near a special solution stay near it, and when is a flow determined by its data? Start with: Uniqueness of the Ricci Flow on Complete Noncompact Manifolds (Chen et al., 2005)

In the guidebook

  1. 12C.9
    After PerelmanBook 12C · Extinction and the Proof

    Singular flows, the Smale conjecture, and Bamler’s theory.

  2. 5A.5
    Uniformization and the Two-Dimensional Ricci FlowBook 5A · Complex Analysis and Conformal Geometry

    Constant-curvature metrics on surfaces, and Ricci flow as a heat equation for the conformal factor.

  3. 10A.12
    Curve Shortening and Minimal DiscsBook 10A · Three-Manifolds and Geometrization

    How loops shrink under curvature, how the discs they bound lose area, and Perelman's extinction estimate.