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Variational theory for the total scalar curvature functional for riemannian metrics and related topics
- Publisher
- Springer Journals
- Copyright
- Copyright © Springer-Verlag Berlin Heidelberg 2003
- Subject
- Legacy
- ISSN
- 0025-5874
- eISSN
- 1432-1823
- DOI
- 10.1007/s00209-002-0486-7
- Publisher site
- See Article on Publisher Site
Abstract
. This paper is devoted to the study of a problem arising from a geometric context, namely the conformal deformation of a Riemannian metric to a scalar flat one having constant mean curvature on the boundary. By means of blow-up analysis techniques and the Positive Mass Theorem, we show that on locally conformally flat manifolds with umbilic boundary all metrics stay in a compact set with respect to the C2-norm and the total Leray-Schauder degree of all solutions is equal to -1. Then we deduce from this compactness result the existence of at least one solution to our problem.Mathematics Subject Classification (2000): 35J60, 53C21, 58G30
Journal
Mathematische Zeitschrift – Springer Journals
Published: May 1, 2003
Keywords: Subject Classification; Riemannian Metrics; Positive Mass Theorem; Flat Manifold; Conformal Deformation