On the umbilic set of immersed surfaces in three-dimensional space forms

被引：0

作者：

Catino, Giovanni ^{[1
]}

Roncoroni, Alberto ^{[2
]}

Vezzoni, Luigi ^{[3
]}

机构：

[1] Politecn Milan, Dipartimento Matemat, Piazza Leonardo da Vinci 32, I-20133 Milan, Italy

[2] Univ Firenze, Dipartimento Matemat & Informat U Dini, Viale Morgagni 67-A, I-50134 Florence, Italy

[3] Univ Torino, Dipartimento Matemat G Peano, Via Carlo Alberto 10, I-10123 Turin, Italy

来源：

BULLETIN DES SCIENCES MATHEMATIQUES | 2020年 / 165卷

关键词：

Immersed surfaces; Hopf theorem; Mean curvature; CONSTANT MEAN-CURVATURE; HYPERSURFACES;

D O I：

10.1016/j.bulsci.2020.102917

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove that, under some integral inequality regarding the mean curvature and the traceless second fundamental form, the set of umbilical points of an immersed surface in a 3-dimensional space form has positive measure. In case of an immersed sphere our result can be seen as a generalization of the celebrated Hopf theorem. (C) 2020 Elsevier Masson SAS. All rights reserved.

引用

页数：7

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