The vanishing of the fundamental gap of convex domains in $\mathbb H^n$
Preprint
Abstract
For the Laplace operator with Dirichlet boundary conditions on convex domains in $\mathbb H^n$, $n\geq 2$, we prove that the product of the fundamental gap with the square of the diameter can be arbitrarily small for domains of any diameter.
Keywords
All Related Versions
This publication has 7 references indexed in Scilit:
- Explicit fundamental gap estimates for some convex domains in $\mathbb{H}^2$Mathematical Research Letters, 2021
- Sharp fundamental gap estimate on convex domains of sphereJournal of Differential Geometry, 2019
- Lower bounds for the first Dirichlet eigenvalue of the Laplacian for domains in hyperbolic spaceMathematical Proceedings of the Cambridge Philosophical Society, 2015
- Proof of the fundamental gap conjectureJournal of the American Mathematical Society, 2011
- On the lowest eigenvalue of the Hodge Laplacian on compact, negatively curved domainsAnnals of Global Analysis and Geometry, 2008
- A second eigenvalue bound for the Dirichlet Laplacian in hyperbolic spaceDuke Mathematical Journal, 2007
- A counterexample to the convexity property of the first eigenfunction on a convex domain of negative curvatureCommunications in Partial Differential Equations, 1989