Embedded isolated singularities of flat surfaces in hyperbolic 3-space

被引：36

作者：

Gálvez, JA ^{[1
]}

Mira, P

机构：

[1] Univ Granada, Dept Geometria & Topol, E-18071 Granada, Spain

[2] Univ Politecn Cartagena, Dept Matemat Aplicada & Estadist, Murcia 30203, Spain

来源：

CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS | 2005年 / 24卷 / 02期

关键词：

D O I：

10.1007/s00526-004-0321-6

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We give a complete description of the flat surfaces in hyperbolic 3-space that are regularly embedded around an isolated singularity. Specifically, we show that there is a one-to-one explicit correspondence between this class and the class of regular analytic convex Jordan curves in the 2-sphere. Previously, the only known examples of such surfaces were rotational ones. To achieve this result, we first solve the geometric Cauchy problem for flat surfaces in hyperbolic 3-space.

引用

页码：239 / 260

页数：22

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