How close is too close for singular mean curvature flows?

IF 2.1 2区数学 Q1 MATHEMATICS

Calculus of Variations and Partial Differential Equations Pub Date : 2026-01-01 Epub Date: 2026-07-18 DOI:10.1007/s00526-026-03403-4

J M Daniels-Holgate, Or Hershkovits

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引用次数: 0

Abstract

Suppose ${(M_{t}^{i})}_{t \in [0, T)}$ , $i = 1, 2$ , are two mean curvature flows in $R^{n + 1}$ encountering a multiplicity one compact singularity at time T, in such a manner that for every k, the Hausdorff distance between the two flows, $d_{H}$ , satisfies $d_{H} (M_{t}^{1}, M_{t}^{2}) / {(T - t)}^{k} \to 0$ . We demonstrate that $M_{t}^{1} = M_{t}^{2}$ for every t. This generalizes a result of Martin-Hagemayer and Sesum, who proved the case where $M_{t}^{1}$ is itself a self-similarly shrinking flow.

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对于奇异平均曲率流来说，多近才算太近？

假设（M ti） t∈[0,t), i = 1,2，是R n + 1中的两个平均曲率流，在时间t遇到多重紧奇点1，这样对于每k，两个流之间的Hausdorff距离dh满足dh (M t 1, M t 2) / (t - t) k→0。我们证明了M t1 = M t2对于每一个t。这推广了Martin-Hagemayer和Sesum的结果，他们证明了M t1本身是一个自相似收缩流的情况。

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.