毛细超曲面的完全非线性局部约束曲率流

IF 0.6 3区数学 Q3 MATHEMATICS

Annals of Global Analysis and Geometry Pub Date : 2025-01-03 DOI:10.1007/s10455-024-09983-8

Xinqun Mei, Liangjun Weng

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引用次数: 0

摘要

本文研究了半空间中凸毛细超曲面的局部约束全非线性曲率流。我们证明了流保持了凸性，一直存在，并平滑地收敛到一个球形帽。这可以看作是Mei等人的结果的完全非线性对应（Int Math Res Not IMRN 1:152-174, 2024）。作为副产物，高阶毛细管等周比（1.6）沿此流单调演化，从而产生一类Alexandrov-Fenchel不等式。

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A fully nonlinear locally constrained curvature flow for capillary hypersurface

In this article, we study a locally constrained fully nonlinear curvature flow for convex capillary hypersurfaces in half-space. We prove that the flow preserves the convexity, exists for all time, and converges smoothly to a spherical cap. This can be viewed as the fully nonlinear counterpart of the result in Mei et al. (Int Math Res Not IMRN 1:152–174, 2024). As a byproduct, a high-order capillary isoperimetric ratio (1.6) evolves monotonically along this flow, which yields a class of the Alexandrov–Fenchel inequalities.

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来源期刊

Annals of Global Analysis and Geometry 数学-数学

CiteScore

1.20

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： This journal examines global problems of geometry and analysis as well as the interactions between these fields and their application to problems of theoretical physics. It contributes to an enlargement of the international exchange of research results in the field. The areas covered in Annals of Global Analysis and Geometry include: global analysis, differential geometry, complex manifolds and related results from complex analysis and algebraic geometry, Lie groups, Lie transformation groups and harmonic analysis, variational calculus, applications of differential geometry and global analysis to problems of theoretical physics.