Isolated singularities of graphs in warped products and Monge-Ampere equations

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:260

Article

Galvez, Jose A.¹  Jimenez, Asun²  Mira, Pablo³ 

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

[2] Univ Fed Fluminense, Dept Geometria, IME, BR-24020140 Niteroi, RJ, Brazil

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

关键词: Isolated singularities;    Convex graphs;    Monge-Ampere equation;    Warped products;    Prescribed curvature;   

DOI  :  10.1016/j.jde.2015.09.061

来源: Elsevier

【 摘 要 】

We study graphs of positive extrinsic curvature with a non-removable isolated singularity in 3-dimensional warped product spaces, and describe their behavior at the singularity in several natural situations. We use Monge Ampere equations to give a classification of the surfaces in 3-dimensional space forms which are embedded around a non-removable isolated singularity and have a prescribed, real analytic, positive extrinsic curvature function at every point. Specifically, we prove that this space is in one-to-one correspondence with the space of regular, analytic, strictly convex Jordan curves in the 2-dimensional sphere S-2. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

Free