On the Spectral Gap for Convex Domains
Spectral Theory
2007-05-23 v1 Mathematical Physics
math.MP
Probability
Abstract
We prove the following for a bounded convex planar domain that is symmetric with respect to both coordinate axes. Consider a centered rectangle with sides parallel to the axes that strictly contains the domain. If the domain is not a certain kind of rectangle, the spectral gap of the domain is larger than the spectral gap of the rectangle. We also provide explicit lower bounds for the differnce between the gaps.
Cite
@article{arxiv.math/0607219,
title = {On the Spectral Gap for Convex Domains},
author = {Burgess Davis and Majid Hosseini},
journal= {arXiv preprint arXiv:math/0607219},
year = {2007}
}
Comments
18 pages