单位球中自由边界超曲面沿反向平均曲率流的第一特征值

IF 0.6 4区数学 Q3 MATHEMATICS

Differential Geometry and its Applications Pub Date : 2023-12-13 DOI:10.1016/j.difgeo.2023.102095

Pak Tung Ho , Juncheol Pyo

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引用次数: 0

摘要

在本论文中，我们考虑了单位球中自由边界适当超曲面上 p-Laplacian 的第一个非零特征值 λp,1 沿着反平均曲率流演化的问题。我们证明了λp,1 沿流动单调递减。利用单位球中自由边界圆盘的收敛性，我们给出了单位球中自由边界圆盘型超曲面的 λp,1 下限。

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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First eigenvalues of free boundary hypersurfaces in the unit ball along the inverse mean curvature flow

In this note, we consider the first nonzero eigenvalue $λ_{p, 1}$ of the p-Laplacian on free boundary proper hypersurfaces in the unit ball evolving along the inverse mean curvature flow. We show that $λ_{p, 1}$ is monotone decreasing along the flow. Using the convergence of free boundary disks in the unit ball, we give a lower bound of $λ_{p, 1}$ of a free boundary disk type hypersurface in the unit ball.

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来源期刊

Differential Geometry and its Applications 数学-数学

CiteScore

1.00

自引率

20.00%

发文量

审稿时长

6-12 weeks

期刊介绍： Differential Geometry and its Applications publishes original research papers and survey papers in differential geometry and in all interdisciplinary areas in mathematics which use differential geometric methods and investigate geometrical structures. The following main areas are covered: differential equations on manifolds, global analysis, Lie groups, local and global differential geometry, the calculus of variations on manifolds, topology of manifolds, and mathematical physics.