Paper · May 17, 2024

A convergence result for Mean Curvature Flow of totally real submanifolds

Tristan C. Collins, Adam Jacob, Yu-Shen Lin

math.DGWider flowsarXiv:2405.11049
PDF Abstract page

As on arXiv

Abstract

We establish a convergence result for the mean curvature flow starting from a totally real submanifold which is "almost minimal" in a precise, quantitative sense. This extends, and makes effective, a result of H. Li for the Lagrangian mean curvature flow.

Comments: 41 pages

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 Mean Curvature Flows of Two-Convex Lagrangians (Chung-Jun Tsai, Mao-Pei Tsui and Mu-Tao Wang, 2023)4Tsai 2023 Entire solutions of two-convex Lagrangian mean curvature flows (Chung-Jun Tsai, Mao-Pei Tsui and Mu-Tao Wang, 2023)3Tsai 2023 Singularity formation along the line bundle mean curvature flow (Yu Hin Chan and Adam Jacob, 2023)2Chan 2023 Stability of the generalized Lagrangian mean curvature flow in cotangent bundle (Xishen Jin and Jiawei Liu, 2024)6Jin 2024 A Priori Estimates for Singularities of the Lagrangian Mean Curvature Flow with Supercritical Phase (Arunima Bhattacharya and Jeremy Wall, 2024)7Bhattacharya 2024 Lagrangian mean curvature flow of surfaces with mean curvature bound (Sourav Ghosh, 2025)5Ghosh 2025 Almost isoclinic Lagrangian submanifolds (Tang-Kai Lee and Mu-Tao Wang, 2026)1Lee 2026 The mean curvature blows up at nondegenerate neck pinch singularities of Lagrangian mean curvature flow (Jason D. Lotay and Goncalo Oliveira, 2026)8Lotay 2026
Closer to the centre: more closely connected. Clockwise from the top: oldest to newest. Ricci flowWider flowsalso connected to each other
  1. Almost isoclinic Lagrangian submanifolds

    Tang-Kai Lee and Mu-Tao WangWider flows PDF

    Topics Lagrangian mean curvature flow · Shared terms “submanifolds”

  2. Singularity formation along the line bundle mean curvature flow

    Yu Hin Chan and Adam JacobWider flows PDF

    Topics Lagrangian mean curvature flow · Same author Adam Jacob

  3. Entire solutions of two-convex Lagrangian mean curvature flows

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

    Topics Lagrangian mean curvature flow · Shared terms “submanifolds”

  4. Mean Curvature Flows of Two-Convex Lagrangians

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

    Topics Lagrangian mean curvature flow · Shared terms “submanifolds”

  5. Lagrangian mean curvature flow of surfaces with mean curvature bound

    Sourav GhoshWider flows PDF

    Topics Lagrangian mean curvature flow

  6. Stability of the generalized Lagrangian mean curvature flow in cotangent bundle

    Xishen Jin and Jiawei LiuWider flows PDF

    Topics Lagrangian mean curvature flow · Shared terms “submanifolds”

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.