Manifolds with weighted Poincaré inequality and uniqueness of minimal hypersurfaces

Details Manifolds with weighted Poincaré inequality and uniqueness of minimal hypersurfaces Manifolds with weighted Poincaré inequality and uniqueness of minimal hypersurfaces

2008-08-08

arxiv.org/abs/0808.1185v1

Mathematics

Differential Geometry

Scientific paper

In this paper, we obtain results on rigidity of complete Riemannian manifolds
with weighted Poincar\'e inequality. As an application, we prove that if $M$ is
a complete $\frac{n-2}{n}$-stable minimal hypersurface in $\mathbb{R}^{n+1}$
with $n\geq 3$ and has bounded norm of the second fundamental form, then $M$
must either have only one end or be a catenoid.

Affiliated with

Also associated with

No associations

Rating

Manifolds with weighted Poincaré inequality and uniqueness of minimal hypersurfaces 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 Manifolds with weighted Poincaré inequality and uniqueness of minimal hypersurfaces, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Manifolds with weighted Poincaré inequality and uniqueness of minimal hypersurfaces will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-29552