- 99-32 Exner P., Harrell E.M., Loss M.
- Optimal eigenvalues for some Laplacians and Schr\"odinger operators
depending on curvature.
(34K, plain TeX)
Jan 26, 99
(auto. generated ps),
of related papers
Abstract. This article is an expanded version of the plenary talk
given by Evans Harrell at QMath98, a meeting in Prague, June, 1998.
We consider Laplace operators and Schr\"odinger operators with potentials
containing curvature on certain regions of nontrivial topology, especially
closed curves, annular domains, and shells. Dirichlet boundary conditions
are imposed on any boundaries. Under suitable assumptions
we prove that the fundamental eigenvalue is maximized when the geometry
We also comment on the use of coordinate transformations for these
operators and mention some open problems.