Embedded isolated singularities of flat surfaces in hyperbolic 3-space

被引：0
作者：
José A. Gálvez
Pablo Mira
机构：
[1] Universidad de Granada,Departamento de Geometría y Topología
[2] Universidad Politécnica de Cartagena,Departamento de Matemática Aplicada y Estadística
来源：
Calculus of Variations and Partial Differential Equations | 2005年 / 24卷
关键词：
Cauchy Problem; System Theory; Flat Surface; Analytic Convex; Jordan Curve;
D O I：
暂无
中图分类号：
学科分类号：
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.
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页码：239 / 260
页数：21
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