Paper · May 20, 2016

Surfaces of Co-dimension Two Pinched by Normal Curvature

Charles Baker, Huy The Nguyen

math.DGWider flowsarXiv:1605.06200
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As on arXiv

Abstract

We prove that codimension two surfaces satisfying a nonlinear curvature condition depending on normal curvature are smoothly deformed by mean curvature flow to round points.

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Submitted
May 20, 2016
Subjects
math.DG
Mean curvature flow

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 Pinched Ancient Solutions to the High Codimension Mean Curvature Flow (Stephen Lynch and Huy The Nguyen, 2017)3Lynch 2017 Cylindrical Estimates for High Codimension Mean Curvature Flow (Huy The Nguyen, 2018)6Nguyen 2018 High Codimension Mean Curvature Flow with Surgery (Stephen Lynch and Huy The Nguyen, 2020)8Lynch 2020 Evolving Pinched Submanifolds of the Sphere by Mean Curvature Flow (Charles Baker and Huy The Nguyen, 2020)1Baker 2020 Surfaces pinched by normal curvature for mean curvature flow in space forms (Dong Pu, Jingjing Su and Hongwei Xu, 2020)2Pu 2020 Convexity Estimates for High Codimension Mean Curvature Flow (Stephen Lynch and Huy The Nguyen, 2020)7Lynch 2020 Quadratically pinched hypersurfaces of the sphere via mean curvature flow with surgery (Mat Langford and Huy The Nguyen, 2020)5Langford 2020 Quadratically pinched submanifolds of the sphere via mean curvature flow with surgery (Mat Langford, Stephen Lynch and Huy The Nguyen, 2021)4Langford 2021
Closer to the centre: more closely connected. Clockwise from the top: oldest to newest. Ricci flowWider flowsalso connected to each other
  1. Evolving Pinched Submanifolds of the Sphere by Mean Curvature Flow

    Charles Baker and Huy The NguyenWider flows

    Topics Mean curvature flow · Same authors Charles Baker, Huy The Nguyen · Shared terms “normal curvature”, “curvature condition”, “round point”

  2. Surfaces pinched by normal curvature for mean curvature flow in space forms

    Dong Pu, Jingjing Su and Hongwei XuWider flows

    Topics Mean curvature flow · Shared terms “normal curvature”

  3. Pinched Ancient Solutions to the High Codimension Mean Curvature Flow

    Stephen Lynch and Huy The NguyenWider flows

    Topics Mean curvature flow · Same author Huy The Nguyen · Shared terms “round point”

  4. Quadratically pinched submanifolds of the sphere via mean curvature flow with surgery

    Mat Langford, Stephen Lynch and Huy The NguyenWider flows

    Topics Mean curvature flow · Same author Huy The Nguyen

  5. Quadratically pinched hypersurfaces of the sphere via mean curvature flow with surgery

    Mat Langford and Huy The NguyenWider flows

    Topics Mean curvature flow · Same author Huy The Nguyen

  6. Cylindrical Estimates for High Codimension Mean Curvature Flow

    Huy The NguyenWider flows

    Topics Mean curvature flow · Same author Huy The Nguyen · Shared terms “curvature condition”

  7. Convexity Estimates for High Codimension Mean Curvature Flow

    Stephen Lynch and Huy The NguyenWider flows

    Topics Mean curvature flow · Same author Huy The Nguyen

  8. High Codimension Mean Curvature Flow with Surgery

    Stephen Lynch and Huy The NguyenWider flows

    Topics Mean curvature flow · Same author Huy The Nguyen

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.

Mean curvature flow Wider flows A hypersurface moves in the direction of its mean curvature vector, which decreases area as fast as possible in the L² sense. Start with: Flow by mean curvature of convex surfaces into spheres (Huisken, 1984)

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.