Pinched hypersurfaces are compact-Reference-Cited by-同舟云学术

Pinched hypersurfaces are compact

Published:2023-01-01 Issue:1 Volume:23 Page:
ISSN:2169-0375
Container-title:Advanced Nonlinear Studies
language:en
Short-container-title:

Author:

Bourni Theodora¹,Langford Mat²,Lynch Stephen³

Affiliation:

1. Department of Mathematics, University of Tennessee Knoxville , Knoxville TN , 37996-1320, Tennessee , United States

2. School of Mathematical and Physical Sciences, The University of Newcastle , Newcastle , NSW, 2308 , Australia

3. Eberhard Karls Universität Tübingen, Fachbereich Mathematik, Auf der Morgenstelle 10 , 72076 Tübingen , Germany

Abstract

Abstract We make rigorous and old idea of using mean curvature flow to prove a theorem of Richard Hamilton on the compactness of proper hypersurfaces with pinched, bounded curvature.

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics,Statistical and Nonlinear Physics

Link

https://www.degruyter.com/document/doi/10.1515/ans-2022-0046/pdf

Reference21 articles.

1. A. Deruelle, F. Schulze, and M. Simon, Initial stability estimates for Ricci flow and three dimensional Ricci-pinched manifolds, Preprint, https://arxiv.org/abs/2203.15313.

2. B. Andrews and C. Baker, Mean curvature flow of pinched submanifolds to spheres, J. Differential Geom. 85 (2010), no. 3, 357–395.

3. B. Andrews, B. Chow, C. Guenther, and M. Langford, Extrinsic geometric flows, 1st edition, vol. 206, Graduate Studies in Mathematics, American Mathematical Society, Providence, RI, 2020.

4. C. Böhm and B. Wilking, Manifolds with positive curvature operators are space forms, Ann. of Math. (2), 167 (2008), no. 3, 1079–1097.

5. T. Bourni and M. Langford, Type-II singularities of two-convex immersed mean curvature flow, Geom. Flows 2 (2017), 1–17.

Cited by 1 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. Local convexity estimates for mean curvature flow;Journal für die reine und angewandte Mathematik (Crelles Journal);2023-04-27