Smooth Compactness for Spaces of Asymptotically Conical Self-Expanders of Mean Curvature Flow-Reference-Cited by-同舟云学术

Smooth Compactness for Spaces of Asymptotically Conical Self-Expanders of Mean Curvature Flow

Published:2019-05-20 Issue:12 Volume:2021 Page:9016-9044
ISSN:1073-7928
Container-title:International Mathematics Research Notices
language:en
Short-container-title:

Author:

Bernstein Jacob¹,Wang Lu²

Affiliation:

1. Department of Mathematics, Johns Hopkins University, N. Charles Street, Baltimore, MD, USA

2. Department of Mathematics, University of Wisconsin-Madison, Lincoln Drive, Madison, WI, USA

Abstract

Abstract We show compactness in the locally smooth topology for certain natural families of asymptotically conical self-expanding solutions of mean curvature flow. Specifically, we show such compactness for the set of all 2D self-expanders of a fixed topological type and, in all dimensions, for the set of self-expanders of low entropy and for the set of mean convex self-expanders with strictly mean convex asymptotic cones. From this we deduce that the natural projection map from the space of parameterizations of asymptotically conical self-expanders to the space of parameterizations of the asymptotic cones is proper for these classes.

Funder

National Science Foundation

Alfred P. Sloan Foundation

Office of the Vice Chancellor for Research and Graduate Education, University of Wisconsin-Madison

Wisconsin Alumni Research Foundation

University of Wisconsin-Madison

Publisher

Oxford University Press (OUP)

Subject

General Mathematics

Link

http://academic.oup.com/imrn/article-pdf/2021/12/9016/38814295/rnz087.pdf

Reference33 articles.

1. A computed example of non-uniqueness of mean curvature flow in ${\mathbb{R}}^3$;Angenent,1995

2. An integer degree for the space of asymptotically conical self-expanders of mean curvature flow;Bernstein

3. The space of asymptotically conical self-expanders of mean curvature flow;Bernstein

4. Lecture Notes in Mathematics;Cerf,1968

5. La stratification naturelle des espaces de fonctions différentiables réelles et le théorème de la pseudo-isotopie;Cerf;Inst. Hautes Études Sci. Publ. Math.,1970

Cited by 17 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. A rigidity theorem for self-expanders;manuscripta mathematica;2024-06-03

2. Mean curvature flow with generic initial data;Inventiones mathematicae;2024-04-23

3. Mean Convex Smoothing of Mean Convex Cones;Geometric and Functional Analysis;2024-02

4. An integer degree for asymptotically conical self-expanders;Calculus of Variations and Partial Differential Equations;2023-07-22

5. Convexity of 2-Convex Translating and Expanding Solitons to the Mean Curvature Flow in $${{\mathbb {R}}}^{n+1}$$;The Journal of Geometric Analysis;2023-05-22