Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4592800 | Journal of Functional Analysis | 2007 | 11 Pages |
Abstract
On a compact Riemannian manifold (Vn,g) (n>2), a long-standing question is: Does the set of the solutions of the Yamabe equation compact in C0? There are three cases in the Yamabe problem (see Aubin [T. Aubin, Some Nonlinear Problems in Riemannian Geometry, Springer-Verlag, New York, 1998]) according to the sign of the inf of the Yamabe functional. We prove the C0 compactness of the set of the solutions of the Yamabe equation (except on the sphere) in the positive case, the only case which makes difficulties.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory