On the spectrum of $\bar{X}$-bounded minimal submanifolds

Details On the spectrum of $\bar{X}$-bounded minimal submanifolds On the spectrum of $\bar{X}$-bounded minimal submanifolds

2009-01-09

arxiv.org/abs/0901.1246v3

Mathematics

Differential Geometry

v.2 13 pages. We improve some theorems, correct some misprints and add a new theorem (theorem 5) in section 2 that shows compl

Scientific paper

We prove, under a certain boundedness condition at infinity on the $(\bar{X}^{\top}, \bar{X}^{\bot})$-component of the second fundamental form, the vanishing of the essential spectrum of a complete minimal $\bar{X}$-bounded and $\bar{X}$-properly immersed submanifold on a Riemannian manifold endowed with a strongly convex vector field $\bar{X}$. The same conclusion also holds for any complete minimal $h$-bounded and $h$-properly immersed submanifold that lies in a open set of a Riemannian manifold $\oM$ supporting a nonnegative strictly convex function $h$. This extends a recent result of Bessa, Jorge and Montenegro on the spectrum of Martin-Morales minimal surfaces. Our proof uses as main tool an extension of Barta's theorem given in \cite{BM}

Affiliated with

Also associated with

No associations

Rating

On the spectrum of $\bar{X}$-bounded minimal submanifolds 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 the spectrum of $\bar{X}$-bounded minimal submanifolds, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On the spectrum of $\bar{X}$-bounded minimal submanifolds will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-544841