RIGIDITY OF MINIMAL LAGRANGIAN DIFFEOMORPHISMS BETWEEN SPHERICAL CONE SURFACES

被引：0

作者：

El Emam, Christian ^{[1
]}

Seppi, Andrea ^{[2
]}

机构：

[1] Univ Luxembourg, Maison Nombre,6 Ave Fonte, L-4364 Esch Sur Alzette, Luxembourg

[2] Univ Grenoble Alpes, Lab Math, UMR 5582, CS 40700, F-38058 Grenoble 9, France

来源：

JOURNAL DE L ECOLE POLYTECHNIQUE-MATHEMATIQUES | 2022年 / 9卷

关键词：

Spherical surfaces; conical singularities; minimal Lagrangian maps; immersions in Eu-clidean space; isolated singularities; Gaussian curvature; CURVATURE; SINGULARITIES; METRICS;

D O I：

10.5802/jep.190

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove that any minimal Lagrangian diffeomorphism between two closed spherical surfaces with cone singularities is an isometry, without any assumption on the multiangles of the two surfaces. As an application, we show that every branched immersion of a closed surface of constant positive Gaussian curvature in Euclidean three-space is a branched covering onto a round sphere, thus generalizing the classical rigidity theorem of Liebmann to branched immersions.

引用

页码：581 / 600

页数：21

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