Metrics with prescribed Ricci curvature near the boundary of a manifold

Pulemotov, Artem (2013) Metrics with prescribed Ricci curvature near the boundary of a manifold. Mathematische Annalen, 357 3: 969-986. doi:10.1007/s00208-013-0929-y

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Author Pulemotov, Artem
Title Metrics with prescribed Ricci curvature near the boundary of a manifold
Journal name Mathematische Annalen   Check publisher's open access policy
ISSN 0025-5831
1432-1807
Publication date 2013-11-01
Sub-type Article (original research)
DOI 10.1007/s00208-013-0929-y
Volume 357
Issue 3
Start page 969
End page 986
Total pages 18
Place of publication Heidelberg, Germany
Publisher Springer
Language eng
Formatted abstract
Suppose M is a manifold with boundary. Choose a point o ∈ ∂M. We investigate the prescribed Ricci curvature equation Ric(G) = T in a neighborhood of under natural boundary conditions. The unknown G here is a Riemannian metric. The letter T on the right-hand side denotes a (0,2)-tensor. Our main theorems address the questions of the existence and the uniqueness of solutions. We explain, among other things, how these theorems may be used to study rotationally symmetric metrics near the boundary of a solid torus T . The paper concludes with a brief discussion of the Einstein equation on T .
Keyword Einstein Equations
Existence
Spaces
Q-Index Code C1
Q-Index Status Confirmed Code
Institutional Status UQ

Document type: Journal Article
Sub-type: Article (original research)
Collections: School of Mathematics and Physics
Official 2014 Collection
 
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Citation counts: TR Web of Science Citation Count  Cited 2 times in Thomson Reuters Web of Science Article | Citations
Scopus Citation Count Cited 3 times in Scopus Article | Citations
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Created: Sun, 24 Nov 2013, 10:05:28 EST by System User on behalf of School of Mathematics & Physics