The Dirichlet problem for the prescribed Ricci curvature equation on cohomogeneity one manifolds

Pulemotov, Artem (2015) The Dirichlet problem for the prescribed Ricci curvature equation on cohomogeneity one manifolds. Annali di Matematica Pura ed Applicata, 195 4: 1269-1286. doi:10.1007/s10231-015-0515-x


Author Pulemotov, Artem
Title The Dirichlet problem for the prescribed Ricci curvature equation on cohomogeneity one manifolds
Journal name Annali di Matematica Pura ed Applicata   Check publisher's open access policy
ISSN 1618-1891
0373-3114
Publication date 2015-06-27
Sub-type Article (original research)
DOI 10.1007/s10231-015-0515-x
Volume 195
Issue 4
Start page 1269
End page 1286
Total pages 18
Place of publication Heidelberg, Germany
Publisher Springer
Collection year 2016
Language eng
Formatted abstract
Let M be a domain enclosed between two principal orbits on a cohomogeneity one manifold M1. Suppose that T and R are symmetric invariant (0, 2)-tensor fields on M and ∂M, respectively. The paper studies the prescribed Ricci curvature equation Ric(G)=T for a Riemannian metric G on M subject to the boundary condition G∂M=R (the notation G∂M here stands for the metric induced by G on ∂M). Imposing a standard assumption on M1, we describe a set of requirements on T and R that guarantee global and local solvability.
Keyword Ricci curvature
Dirichlet problem
Cohomogeneity one
Q-Index Code C1
Q-Index Status Confirmed Code
Institutional Status UQ
Additional Notes Published online 27 June 2015.

Document type: Journal Article
Sub-type: Article (original research)
Collections: School of Mathematics and Physics
Official 2016 Collection
 
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