Affiliation:
1. Grupo de Física Matemática, Faculdade de Ciências, Universidade de Lisboa , Campo Grande, Edifício C6, 1749-016 Lisboa, Portugal
Abstract
We show the existence of classes of non-tiling domains satisfying Pólya’s conjecture in any dimension, in both the Euclidean and non-Euclidean cases. This is a consequence of a more general observation asserting that if a domain satisfies Pólya’s conjecture eventually, that is, for a sufficiently large order of the eigenvalues, and may be partioned into p non-overlapping isometric sub-domains, with p arbitrarily large, then there exists an order p0 such that for p larger than p0 all such sub-domains satisfy Pólya’s conjecture. In particular, this allows us to show that families of sectors of domains of revolution with analytic boundary, and thin cylinders satisfy Pólya’s conjecture, for instance. We also improve upon the Li–Yau constant for general cylinders in the Dirichlet case.
Funder
Fundação para a ciência e tecnologia, Portugal
Subject
Mathematical Physics,Statistical and Nonlinear Physics
Cited by
3 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献