论文标题
在公制测量时出口时间的光谱范围dirichlet空间和应用
Spectral bounds for exit times on metric measure Dirichlet spaces and applications
论文作者
论文摘要
假设二倍DIRICHLET度量测量空间上的热内核具有下粘结的结合，我们证明在相关扩散过程的生存概率上，渐近的光谱上限。结果，我们可以证明，当且仅当频谱的底部为正时，所有起点上的平均退出时间的至上是有限的。在几种应用中，我们表明，在生存概率上的光谱上限意味着riemannian歧管的热点常数的结合。我们的结果适用于有趣的几何环境，包括亚riemannian歧管和分形。
Assuming the heat kernel on a doubling Dirichlet metric measure space has a sub-Gaussian bound, we prove an asymptotically sharp spectral upper bound on the survival probability of the associated diffusion process. As a consequence, we can show that the supremum of the mean exit time over all starting points is finite if and only if the bottom of the spectrum is positive. Among several applications, we show that the spectral upper bound on the survival probability implies a bound for the Hot Spots constant for Riemannian manifolds. Our results apply to interesting geometric settings including sub-Riemannian manifolds and fractals.
