Paper · Jul 8, 2024

Sharp Interior Gradient Estimate for Area Decreasing Graphical Mean Curvature Flow in Arbitrary Codimension

Jingbo Wan

math.DGWider flowsarXiv:2407.05602
PDF Abstract page

As on arXiv

Abstract

We prove the sharp interior gradient estimate for area decreasing graphical mean curvature flow in arbitrary codimension, which generalizes the result in.

Comments: 21 pages, comments are welcome!

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 Graphical mean curvature flow with bounded bi-Ricci curvature (Renan Assimos, Andreas Savas-Halilaj and Knut Smoczyk, 2022)1Assimos 2022 A New Monotone Quantity in Mean Curvature Flow Implying Sharp Homotopic Criteria (Chung-Jun Tsai, Mao-Pei Tsui and Mu-Tao Wang, 2023)4Tsai 2023 Mean Curvature Flows of Two-Convex Lagrangians (Chung-Jun Tsai, Mao-Pei Tsui and Mu-Tao Wang, 2023)6Tsai 2023 Rigidity of area non-increasing maps (Man-Chun Lee, Luen-Fai Tam and Jingbo Wan, 2023)3Lee 2023 Codimension two mean curvature flow of entire graphs (Andreas Savas-Halilaj and Knut Smoczyk, 2024)2Savas-Halila 2024 Isotropy invariant graphical mean curvature flows in warped products (Naotoshi Fujihara and Naoyuki Koike, 2024)5Fujihara 2024 A delayed interior area-to-height estimate for the Curve Shortening Flow (Arjun Sobnack, 2025)7Sobnack 2025 The Genus-Decreasing Property of Mean Curvature Flow, I (Brian White, 2026)8White 2026
Closer to the centre: more closely connected. Clockwise from the top: oldest to newest. Ricci flowWider flowsalso connected to each other
  1. Graphical mean curvature flow with bounded bi-Ricci curvature

    Renan Assimos, Andreas Savas-Halilaj and Knut SmoczykWider flows PDF

    Topics Mean curvature flow · Shared terms “graphical mean”, “area decreasing”

  2. Codimension two mean curvature flow of entire graphs

    Andreas Savas-Halilaj and Knut SmoczykWider flows PDF

    Topics Mean curvature flow · Shared terms “area decreasing”, “graphical mean”

  3. Rigidity of area non-increasing maps

    Man-Chun Lee, Luen-Fai Tam and Jingbo Wan PDF

    Topics Mean curvature flow · Same author Jingbo Wan · Shared terms “graphical mean”

  4. A New Monotone Quantity in Mean Curvature Flow Implying Sharp Homotopic Criteria

    Chung-Jun Tsai, Mao-Pei Tsui and Mu-Tao WangWider flows PDF

    Topics Mean curvature flow · Shared terms “area decreasing”, “graphical mean”

  5. Isotropy invariant graphical mean curvature flows in warped products

    Naotoshi Fujihara and Naoyuki KoikeWider flows PDF

    Topics Mean curvature flow · Shared terms “graphical mean”

  6. Mean Curvature Flows of Two-Convex Lagrangians

    Chung-Jun Tsai, Mao-Pei Tsui and Mu-Tao WangWider flows PDF

    Topics Mean curvature flow · Shared terms “area decreasing”

  7. The Genus-Decreasing Property of Mean Curvature Flow, I

    Brian WhiteWider flows PDF

    Topics Mean curvature flow · Shared terms “decreasing”

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.

In the guidebook

  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.