Motion of level sets by mean curvature. II

Author:

Evans L. C.,Spruck J.

Abstract

We give a new proof of short time existence for the classical motion by mean curvature of a smooth hypersurface. Our method consists in studying a fully nonlinear uniformly parabolic equation satisfied by the signed distance function to the surface

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Reference6 articles.

1. The Dirichlet problem for nonlinear second-order elliptic equations. III. Functions of the eigenvalues of the Hessian;Caffarelli, L.;Acta Math.,1985

2. Uniqueness and existence of viscosity solutions of generalized mean curvature flow equations;Chen, Yun Gang;J. Differential Geom.,1991

3. Motion of level sets by mean curvature. I;Evans, L. C.;J. Differential Geom.,1991

4. The heat equation shrinking convex plane curves;Gage, M.;J. Differential Geom.,1986

5. Three-manifolds with positive Ricci curvature;Hamilton, Richard S.;J. Differential Geometry,1982

Cited by 77 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. Singular limit of a stochastic Allen-Cahn equation with nonlinear diffusion;Journal of Differential Equations;2024-08

2. Segmentation-based tracking of macrophages in 2D+time microscopy movies inside a living animal;Computers in Biology and Medicine;2023-02

3. Level Set Methods and Lagrangian Interfaces;Applied Mathematical Sciences;2022

4. A mass reducing flow for real-valued flat chains with applications to transport networks;ESAIM: Control, Optimisation and Calculus of Variations;2021

5. Nonlocal diffusion of smooth sets;Mathematics in Engineering;2021

同舟云学术

1.学者识别学者识别

2.学术分析学术分析

3.人才评估人才评估

"同舟云学术"是以全球学者为主线,采集、加工和组织学术论文而形成的新型学术文献查询和分析系统,可以对全球学者进行文献检索和人才价值评估。用户可以通过关注某些学科领域的顶尖人物而持续追踪该领域的学科进展和研究前沿。经过近期的数据扩容,当前同舟云学术共收录了国内外主流学术期刊6万余种,收集的期刊论文及会议论文总量共计约1.5亿篇,并以每天添加12000余篇中外论文的速度递增。我们也可以为用户提供个性化、定制化的学者数据。欢迎来电咨询!咨询电话:010-8811{复制后删除}0370

www.globalauthorid.com

TOP

Copyright © 2019-2024 北京同舟云网络信息技术有限公司
京公网安备11010802033243号  京ICP备18003416号-3