The periodic Plateau problem and its application

IF 0.6 3区数学 Q3 MATHEMATICS

Annals of Global Analysis and Geometry Pub Date : 2025-04-13 DOI:10.1007/s10455-025-09993-0

Jaigyoung Choe

引用次数: 0

Abstract

Given a noncompact disconnected periodic curve \(\Gamma \) of infinite length with two components and no self-intersection in \(\mathbb R^3\), it is proved that there exists a noncompact simply connected periodic minimal surface spanning \(\Gamma \). As an application, it is shown that for any tetrahedron T with dihedral angles \(\le 90^\circ \), there exist four embedded minimal annuli in T, which are perpendicular to \(\partial T\) along their boundary. It is also proved that every Platonic solid of \(\mathbb R^3\) contains a free boundary embedded minimal surface of genus zero.

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周期性高原问题及其应用

给出了一条无限长、两分量且在\(\mathbb R^3\)上无自交的非紧连通周期曲线\(\Gamma \)，证明了它存在一个跨出\(\Gamma \)的非紧连通周期极小曲面。作为一个应用，证明了对于任意具有二面角\(\le 90^\circ \)的四面体T，在T中存在四个嵌入的沿其边界垂直于\(\partial T\)的最小环空。并证明了\(\mathbb R^3\)的每一个柏拉图实体都包含一个自由边界嵌入了一个零属最小曲面。

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

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.