Isoperimetry and the properness of weak inverse mean curvature flow

IF 2.1 2区数学 Q1 MATHEMATICS

Calculus of Variations and Partial Differential Equations Pub Date : 2024-09-18 DOI:10.1007/s00526-024-02832-3

Kai Xu

引用次数: 0

Abstract

We prove a new existence theorem for proper solutions of Huisken and Ilmanen’s weak inverse mean curvature flow, assuming certain non-degeneracy conditions on the isoperimetric profile. In particular, no curvature assumption is imposed in our existence theorem.

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等压法和弱反平均曲率流的适当性

我们为 Huisken 和 Ilmanen 的弱逆平均曲率流的适当解证明了一个新的存在性定理，前提是等周剖面具有某些非退化条件。特别是，我们的存在定理中没有曲率假设。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Calculus of Variations and Partial Differential Equations 数学-数学

CiteScore

3.30

自引率

4.80%

发文量

224

审稿时长

6 months

期刊介绍： Calculus of variations and partial differential equations are classical, very active, closely related areas of mathematics, with important ramifications in differential geometry and mathematical physics. In the last four decades this subject has enjoyed a flourishing development worldwide, which is still continuing and extending to broader perspectives. This journal will attract and collect many of the important top-quality contributions to this field of research, and stress the interactions between analysts, geometers, and physicists. The field of Calculus of Variations and Partial Differential Equations is extensive; nonetheless, the journal will be open to all interesting new developments. Topics to be covered include: - Minimization problems for variational integrals, existence and regularity theory for minimizers and critical points, geometric measure theory - Variational methods for partial differential equations, optimal mass transportation, linear and nonlinear eigenvalue problems - Variational problems in differential and complex geometry - Variational methods in global analysis and topology - Dynamical systems, symplectic geometry, periodic solutions of Hamiltonian systems - Variational methods in mathematical physics, nonlinear elasticity, asymptotic variational problems, homogenization, capillarity phenomena, free boundary problems and phase transitions - Monge-Ampère equations and other fully nonlinear partial differential equations related to problems in differential geometry, complex geometry, and physics.