On a geometric equation with critical nonlinearity on the boundary

Details On a geometric equation with critical nonlinearity on the boundary On a geometric equation with critical nonlinearity on the boundary

2001-06-26

arxiv.org/abs/math/0106219v4

Mathematics

Analysis of PDEs

28 pages

Scientific paper

A theorem of Escobar asserts that, on a positive three dimensional smooth compact Riemannian manifold with boundary which is not conformally equivalent to the standard three dimensional ball, a necessary and sufficient condition for a $C^2$ function $H$ to be the mean curvature of some conformal flat metric is that $H$ is positive somewhere. We show that, when the boundary is umbilic and the function $H$ is positive everywhere, all such metrics stay in a compact set with respect to the $C^2$ norm and the total degree of all solutions is equal to -1.

Affiliated with

Also associated with

No associations

Rating

On a geometric equation with critical nonlinearity on the boundary does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with On a geometric equation with critical nonlinearity on the boundary, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On a geometric equation with critical nonlinearity on the boundary will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-642118