Isometric embeddings of 2-spheres into Schwarzschild manifolds

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• 作者：Armando J. Cabrera Pacheco ; Pengzi Miao
• 关键词：Primary 53C20 ; Secondary 83C99
• 刊名：manuscripta mathematica
• 出版年：2016
• 出版时间：March 2016
• 年：2016
• 卷：149
• 期：3-4
• 页码：459-469
• 全文大小：414 KB
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• 作者单位：Armando J. Cabrera Pacheco (1)
  Pengzi Miao (1)
  
  1. Department of Mathematics, University of Miami, Coral Gables, FL, 33146, USA
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  Algebraic Geometry
  Topological Groups and Lie Groups
  Geometry
  Number Theory
  Calculus of Variations and Optimal Control
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1432-1785

文摘

Let g be a Riemannian metric on the 2-sphere S 2. Results on isometric embeddings of (S 2, g) into a fixed model manifold often have implications in quasi-local mass related problems in general relativity. In this paper, motivated by the definitions of the Brown–York and the Wang–Yau mass, we consider isometric embeddings of (S 2, g) into conformally flat spaces. We prove that if g is close to the standard metric on S 2, then (S 2, g) admits an isometric embedding into any spatial Schwarzschild manifold with small mass. We also give a sufficient condition that ensures isometric embeddings of perturbations of a Euclidean convex surface into \({\mathbb{R}^3}\) equipped with a conformally flat metric. Mathematics Subject Classification Primary 53C20 Secondary 83C99