On the Spectral Gap for Convex Domains
Burgess Davis, Majid Hosseini
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.
Create a lesson
Related papers
Spectra of Non-Self-Adjoint Almost Mathieu Matrices and the Scottish Flag Operator
Simon Becker, Izak Oltman
Band edges of periodic Schrödinger operators are generically isolated and nondegenerate
Zhongkai Tao, Mengxuan Yang
Uniform Non-Localization for Laplace Eigenfunctions on the Equilateral Triangle: Dirichlet, Neumann, and Robin Boundary Conditions
Binh T. Nguyen
Scaling inequalities and limits for clamped plate eigenvalues on geodesic disks
Scott Harman
Non-Elliptic Quadratic PT-Symmetric Operators and Similarity to Self-Adjoint Operators
Stepan Malkov
Complex Analysis in completeness, spectral and scattering problems
Alexei Poltoratski