Isometric embeddings of 2-spheres into Schwarzschild manifolds

Armando J. Cabrera Pacheco, Pengzi Miao

Research output: Contribution to journalArticle

Abstract

Let g be a Riemannian metric on the 2-sphere S2. Results on isometric embeddings of (S2, 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 (S2, g) into conformally flat spaces. We prove that if g is close to the standard metric on S2, then (S2, 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 (Formula presented.) equipped with a conformally flat metric.

Original languageEnglish (US)
Pages (from-to)459-469
Number of pages11
JournalManuscripta Mathematica
Volume149
Issue number3-4
DOIs
StatePublished - Mar 1 2016

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Isometric Embedding
Conformally Flat
Convex Surface
Metric
Riemannian Metric
General Relativity
Euclidean
Perturbation
Sufficient Conditions

Keywords

  • Primary 53C20
  • Secondary 83C99

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Isometric embeddings of 2-spheres into Schwarzschild manifolds. / Cabrera Pacheco, Armando J.; Miao, Pengzi.

In: Manuscripta Mathematica, Vol. 149, No. 3-4, 01.03.2016, p. 459-469.

Research output: Contribution to journalArticle

Cabrera Pacheco, Armando J. ; Miao, Pengzi. / Isometric embeddings of 2-spheres into Schwarzschild manifolds. In: Manuscripta Mathematica. 2016 ; Vol. 149, No. 3-4. pp. 459-469.
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