论文标题
满足Pólya猜想的非欺骗域的家庭
Families of non-tiling domains satisfying Pólya's conjecture
论文作者
论文摘要
我们显示了在欧几里得和非欧几里得案例中，在任何维度上都满足Pólya猜想的非欺骗域的存在。这是由于更一般的观察的结果，即如果一个域最终满足了Pólya的猜想，也就是说，对于足够大的特征值，并且可以将$ p $ p $ p $ p $ p $ p $ p $ p $ subplapping等等距次级分配给$ p $，那么$ p _ $ p _ $ p _ $ p _ $ p _ $ p a $ p_ $ p a $ p {0} $ p_ $ p {$ p {0} $ p_ $ p {0} $ p _ $ p {子域满足了Pólya的猜想。特别是，这使我们能够证明革命领域的家庭家庭具有分析边界的家庭，而薄缸则满足了Pólya的猜想。在Dirichlet情况下，我们还改善了通用圆柱体的Li-Yau常数。
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 partitioned into $p$ non-overlapping isometric sub-domains, with $p$ arbitrarily large, then there exists an order $p_{0}$ such that for $p$ larger than $p_{0}$ 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.
