Paper · Jun 5, 2017

Boundary regularity for mean curvature flows of higher codimension

Qi Ding, J. Jost, Y. L. Xin

math.DGWider flowsarXiv:1706.01412v4
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Abstract

In this paper, we derive global bounds for the Hölder norm of the gradient of solutions of graphic mean curvature flow with boundary of arbitrary codimension.

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Submitted
Jun 5, 2017
Last revised
Dec 20, 2023 (v4)
Subjects
math.DG, math.AP

Comments: 12 pages

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 Existence and non-existence of minimal graphs (Qi Ding, J. Jost and Y. L. Xin, 2017)2Ding 2017 Mean Curvature Flow of Compact Spacelike Submanifolds in Higher Codimension (Brendan Guilfoyle and Wilhelm Klingenberg, 2018)6Guilfoyle 2018 Mean Curvature Flow with Boundary (Brian White, 2019)3White 2019 Regularity of elliptic and parabolic systems (Tobias Holck Colding and William P. Minicozzi, 2019)7Colding 2019 Singularity models of pinched solutions of mean curvature flow in higher codimension (Keaton Naff, 2019)5Naff 2019 A canonical neighborhood theorem for the mean curvature flow in higher codimension (Keaton Naff, 2020)4Naff 2020 Uniqueness of Asymptotically Conical Higher Codimension Self-Shrinkers and Self-Expanders (Ilyas Khan, 2020)8Khan 2020 Curvature estimates of ancient solutions to the mean curvature flow of higher codimension with convex Gauss image (Hongbing Qiu and Y. L. Xin, 2023)1Qiu 2023
Closer to the centre: more closely connected. Clockwise from the top: oldest to newest. Ricci flowWider flowsalso connected to each other
  1. Curvature estimates of ancient solutions to the mean curvature flow of higher codimension with convex Gauss image

    Hongbing Qiu and Y. L. XinWider flows

    Topics Mean curvature flow · Same author Y. L. Xin · Shared terms “higher codimension”

  2. Existence and non-existence of minimal graphs

    Qi Ding, J. Jost and Y. L. XinWider flows

    Topics Mean curvature flow · Same authors Qi Ding, J. Jost, Y. L. Xin

  3. Mean Curvature Flow with Boundary

    Brian WhiteWider flows

    Topics Mean curvature flow · Shared terms “boundary regularity”

  4. A canonical neighborhood theorem for the mean curvature flow in higher codimension

    Keaton NaffWider flows

    Topics Mean curvature flow · Shared terms “higher codimension”

  5. Singularity models of pinched solutions of mean curvature flow in higher codimension

    Keaton NaffWider flows

    Topics Mean curvature flow · Shared terms “higher codimension”

  6. Mean Curvature Flow of Compact Spacelike Submanifolds in Higher Codimension

    Brendan Guilfoyle and Wilhelm KlingenbergWider flows

    Topics Mean curvature flow · Shared terms “higher codimension”

  7. Regularity of elliptic and parabolic systems

    Tobias Holck Colding and William P. MinicozziWider flows

    Topics Mean curvature flow · Shared terms “higher codimension”

  8. Uniqueness of Asymptotically Conical Higher Codimension Self-Shrinkers and Self-Expanders

    Ilyas KhanWider flows

    Topics Mean curvature flow · Shared terms “higher codimension”

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.