Paper · Aug 9, 2016

The extension problem of the mean curvature flow (I)

Haozhao Li, Bing Wang

math.DGWider flowsarXiv:1608.02832v2

As on arXiv

Abstract

We show that the mean curvature blows up at the first finite singular time for a closed smooth embedded mean curvature flow in R^3.

Submitted
Aug 9, 2016
Last revised
Nov 25, 2018 (v2)
Subjects
math.DG

Comments: 45 pages, 4 figures, modified according to the suggestion of the referee report

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 On the structure of Ricci shrinkers (Haozhao Li, Yu Li and Bing Wang, 2018)6Li 2018 On Ilmanen's multiplicity-one conjecture for mean curvature flow with type-I mean curvature (Haozhao Li and Bing Wang, 2018)1Li 2018 Mean curvature flow with multiplicity 2 convergence in ℝ³ (Jingwen Chen and Ao Sun, 2023)8Chen 2023 Singularities of mean curvature flow with bounded mean curvature and Morse index (Yongheng Han, 2025)5Han 2025 Long-time existence of the Calabi flow on Kähler surfaces with bounded Sobolev constants (Haozhao Li, Bing Wang and Kai Zheng, 2026)2Li 2026 Singularities of Mean Curvature Flow with Bounded Total Curvature (Yongheng Han and Zhen Wang, 2026)7Han 2026 Calabi flow on polarized Kähler surfaces (Haozhao Li, Bing Wang and Kai Zheng, 2026)3Li 2026 Convergence of the Calabi flow on Kähler surfaces with bounded Sobolev constants (Haozhao Li, Bing Wang and Kai Zheng, 2026)4Li 2026
Closer to the centre: more closely connected. Clockwise from the top: oldest to newest. Ricci flowWider flowsalso connected to each other
  1. On Ilmanen's multiplicity-one conjecture for mean curvature flow with type-I mean curvature

    Haozhao Li and Bing WangWider flows

    Topics Mean curvature flow · Same authors Haozhao Li, Bing Wang · Shared terms “embedded mean”, “closed smooth”, “smooth embedded”

  2. Singularities of mean curvature flow with bounded mean curvature and Morse index

    Yongheng HanWider flows

    Topics Mean curvature flow · Shared terms “embedded mean”, “closed smooth”, “smooth embedded”

  3. Singularities of Mean Curvature Flow with Bounded Total Curvature

    Yongheng Han and Zhen WangWider flows

    Topics Mean curvature flow · Shared terms “embedded mean”, “singular time”

  4. Mean curvature flow with multiplicity 2 convergence in

    Jingwen Chen and Ao SunWider flows

    Topics Mean curvature flow · Shared terms “smooth embedded”

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  1. 6A.10
    Curve Shortening and the First Geometric FlowsBook 6A · The Heat Equation and Its Relatives

    Shrinking circles, grim reapers, neckpinches and Huisken’s monotonicity, seen in the plane.