Paper · Apr 9, 2018

Singular Ricci flows II

Bruce Kleiner, John Lott

math.DGarXiv:1804.03265v2
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Abstract

We establish several quantitative results about singular Ricci flows, including estimates on the curvature and volume, and the set of singular times.

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Submitted
Apr 9, 2018
Last revised
Nov 18, 2018 (v2)
Subjects
math.DG

Comments: final version

Ricci flowWeak & singular flows

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 2016, 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 Notes on Perelman's papers (Bruce Kleiner and John Lott, 2006)7Kleiner 2006 Singular Ricci flows I (Bruce Kleiner and John Lott, 2014)1Kleiner 2014 On the rotational symmetry of 3-dimensional κ-solutions (Richard H. Bamler and Bruce Kleiner, 2019)4Bamler 2019 Bounded Ricci Curvature and Positive Scalar Curvature under Singular Ricci de Turck Flow (Klaus Kroencke, Tobias Marxen and Boris Vertman, 2020)8Kroencke 2020 Producing 3d Ricci flows with non-negative Ricci curvature via singular Ricci flows (Yi Lai, 2020)2Lai 2020 Uniqueness and stability of singular Ricci flows in higher dimensions (Robert Haslhofer, 2021)5Haslhofer 2021 Pseudolocality and completeness for nonnegative Ricci curvature limits of 3D singular Ricci flows (Albert Chau and Adam Martens, 2023)6Chau 2023 Singular Ricci Flows on surfaces with boundary and positive scalar curvature (Jean C. Cortissoz and Juan J. Villamarín, 2023)3Cortissoz 2023
Closer to the centre: more closely connected. Clockwise from the top: oldest to newest. Ricci flowWider flowsalso connected to each other
  1. Singular Ricci flows I

    Bruce Kleiner and John LottThe canon

    Topics Weak & singular flows · Same authors Bruce Kleiner, John Lott

  2. Producing 3d Ricci flows with non-negative Ricci curvature via singular Ricci flows

    Yi Lai

    Topics Weak & singular flows

  3. Singular Ricci Flows on surfaces with boundary and positive scalar curvature

    Jean C. Cortissoz and Juan J. Villamarín

    Topics Weak & singular flows

  4. On the rotational symmetry of 3-dimensional -solutions

    Richard H. Bamler and Bruce Kleiner

    Topics Weak & singular flows · Same author Bruce Kleiner

  5. Uniqueness and stability of singular Ricci flows in higher dimensions

    Robert Haslhofer

    Topics Weak & singular flows

  6. Pseudolocality and completeness for nonnegative Ricci curvature limits of 3D singular Ricci flows

    Albert Chau and Adam Martens

    Topics Weak & singular flows

  7. Notes on Perelman's papers

    Bruce Kleiner and John LottThe canon

    Topics Ricci flow · Same authors Bruce Kleiner, John Lott

  8. Bounded Ricci Curvature and Positive Scalar Curvature under Singular Ricci de Turck Flow

    Klaus Kroencke, Tobias Marxen and Boris Vertman

    Topics Weak & singular flows

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)

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.