arXiv Analytics

Sign in

arXiv:0906.0927 [math.DG]AbstractReferencesReviewsResources

A compactness theorem for scalar-flat metrics on manifolds with boundary

Sergio Almaraz

Published 2009-06-04, updated 2010-12-23Version 3

Let (M,g) be a compact Riemannian manifold with boundary. This paper is concerned with the set of scalar-flat metrics which are in the conformal class of g and have the boundary as a constant mean curvature hypersurface. We prove that this set is compact for dimensions greater than or equal to 7 under the generic condition that the trace-free 2nd fundamental form of the boundary is nonzero everywhere.

Comments: 49 pages. Final version, to appear in Calc. Var. Partial Differential Equations
Journal: Calc. Var. Partial Differential Equations 41(3), 341-386 (2011)
Categories: math.DG, math.AP
Subjects: 53C21, 35J65
Related articles: Most relevant | Search more
arXiv:1010.0336 [math.DG] (Published 2010-10-02)
Critical functions and elliptic PDE on compact riemannian manifolds
arXiv:0710.1396 [math.DG] (Published 2007-10-07)
The isoperimetric profile of a compact Riemannian Manifold for small volumes
arXiv:0907.1440 [math.DG] (Published 2009-07-09)
Gradient estimate for the Poisson equation and the non-homogeneous heat equation on compact Riemannian manifolds

Links

Toolbox