Critical points of Green's functions on complete manifolds

Details Critical points of Green's functions on complete manifolds Critical points of Green's functions on complete manifolds

2010-05-28

arxiv.org/abs/1005.5233v1

Mathematics

Differential Geometry

29 pages

Scientific paper

We prove that the number of critical points of a Li-Tam Green's function on a complete open Riemannian surface of finite type admits a topological upper bound, given by the first Betti number of the surface. In higher dimensions, we show that there are no topological upper bounds on the number of critical points by constructing, for each nonnegative integer $N$, a manifold diffeomorphic to $\RR^n$ ($n \geq 3$) whose minimal Green's function has at least $N$ nondegenerate critical points. Variations on the method of proof of the latter result yield contractible $n$-manifolds whose minimal Green's functions have level sets diffeomorphic to any fixed codimension $1$ compact submanifold of $\RR^n$.

Affiliated with

Also associated with

No associations

Rating

Critical points of Green's functions on complete manifolds 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 Critical points of Green's functions on complete manifolds, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Critical points of Green's functions on complete manifolds will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-15727