Existence of the spectral gap for elliptic operators

Details Existence of the spectral gap for elliptic operators Existence of the spectral gap for elliptic operators

1998-04-14

arxiv.org/abs/math/9804151v1

Mathematics

Differential Geometry

Scientific paper

10.1007/BF02412223

Let $M$ be a connected, noncompact, complete Riemannian manifold, consider the operator $L=\DD +\nn V$ for some $V\in C^2(M)$ with $\exp[V]$ integrable w.r.t. the Riemannian volume element. This paper studies the existence of the spectral gap of $L$. As a consequence of the main result, let $\rr$ be the distance function from a point $o$, then the spectral gap exists provided $\lim_{\rr\to\infty}\sup L\rr<0$ while the spectral gap does not exist if $o$ is a pole and $\lim_{\rr\to\infty}\inf L\rr\ge 0.$ Moreover, the elliptic operators on $\mathbb R^d$ are also studied.

Affiliated with

Also associated with

No associations

Rating

Existence of the spectral gap for elliptic operators 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 Existence of the spectral gap for elliptic operators, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Existence of the spectral gap for elliptic operators will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-232184