Paper · May 13, 2022

Entire self-expanders for power of curvature flow in Minkowski space

Zhizhang Wang, Ling Xiao

math.DGWider flowsarXiv:2205.06853
PDF Abstract page

As on arXiv

Abstract

In [19], we prove that if an entire, spacelike, convex hypersurface has bounded principal curvatures, then the (power of ) curvature flow starting from admits a smooth convex solution for Moreover, after rescaling, the flow converges to a convex self-expander that satisfies Unfortunately, the existence of self-expander for power of curvature flow in Minkowski space has not been studied before. In this paper, we fill the gap.

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 Entire convex curvature flow in Minkowski space (Zhizhang Wang and Ling Xiao, 2022)2Wang 2022 Entire σₖ curvature flow in Minkowski space (Zhizhang Wang and Ling Xiao, 2022)1Wang 2022 Self-expanders to the mean curvature flow based on the generalized Lawson-Osserman cone (Chen-Kuan Lee, 2022)8Lee 2022 Invariant λ-translators in Lorentz-Minkowski space (Antonio Bueno and Irene Ortiz, 2024)6Bueno 2024 Translating solutions and the entire Hessian curvature flow in Minkowski space (Qu Changzheng, Wang Zhizhang and Wo Weifeng, 2024)4Changzheng 2024 Convexity of mean convex asymptotically conical self-expanders to the mean curvature flow (Junming Xie, 2025)5Xie 2025 Inverse Hessian Curvature Flow in Minkowski Space I: Cocompact Hypersurfaces (Dake Li, Zhizhang Wang and Shiqi Yin, 2026)7Li 2026 Inverse Hessian Curvature Flow in Minkowski Space II: The Dirichlet problem at infinity (Dake Li, Zhizhang Wang and Shiqi Yin, 2026)3Li 2026
Closer to the centre: more closely connected. Clockwise from the top: oldest to newest. Ricci flowWider flowsalso connected to each other
  1. Entire curvature flow in Minkowski space

    Zhizhang Wang and Ling XiaoWider flows PDF

    Topics Physics, Self-shrinkers & translators, Other curvature flows · Same authors Zhizhang Wang, Ling Xiao · Shared terms “Minkowski space”, “self expanders”, “flow converges”

  2. Entire convex curvature flow in Minkowski space

    Zhizhang Wang and Ling XiaoWider flows PDF

    Topics Physics, Self-shrinkers & translators, Other curvature flows · Same authors Zhizhang Wang, Ling Xiao · Shared terms “Minkowski space”, “self expanders”, “flow converges”

  3. Inverse Hessian Curvature Flow in Minkowski Space II: The Dirichlet problem at infinity

    Dake Li, Zhizhang Wang and Shiqi YinWider flows PDF

    Topics Physics, Self-shrinkers & translators, Other curvature flows · Same author Zhizhang Wang · Shared terms “Minkowski space”, “convex self”, “spacelike”

  4. Translating solutions and the entire Hessian curvature flow in Minkowski space

    Qu Changzheng, Wang Zhizhang and Wo WeifengWider flows PDF

    Topics Physics, Self-shrinkers & translators, Other curvature flows · Shared terms “Minkowski space”, “flow converges”, “spacelike”

  5. Convexity of mean convex asymptotically conical self-expanders to the mean curvature flow

    Junming XieWider flows PDF

    Topics Self-shrinkers & translators · Shared terms “self expanders”, “convex self”

  6. Invariant -translators in Lorentz-Minkowski space

    Antonio Bueno and Irene OrtizWider flows PDF

    Topics Physics, Self-shrinkers & translators · Shared terms “Minkowski space”, “spacelike”

  7. Inverse Hessian Curvature Flow in Minkowski Space I: Cocompact Hypersurfaces

    Dake Li, Zhizhang Wang and Shiqi YinWider flows PDF

    Topics Other curvature flows · Same author Zhizhang Wang · Shared terms “Minkowski space”

  8. Self-expanders to the mean curvature flow based on the generalized Lawson-Osserman cone

    Chen-Kuan LeeWider flows PDF

    Topics Self-shrinkers & translators · Shared terms “self expanders”

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.