论文标题
快速体积增长和容量估计的几何影响
Geometric implications of fast volume growth and capacity estimates
论文作者
论文摘要
我们获得了Annuli的连通性，以使体积的度量达到一倍，该量度达到了庞加莱不平等，容量估计和快速体积生长条件的元素。 Grigor'yan和Saloff-Coste引入了这种类型的连通性，以获得Harnack不平等的稳定结果，并研究末端的歧管上的扩散。作为我们结果的应用，我们在带有径向型重量的Dirichlet形式的扰动下获得了椭圆形harnack不等式的稳定性。
We obtain connectivity of annuli for a volume doubling metric measure Dirichlet space which satisfies a Poincaré inequality, a capacity estimate and a fast volume growth condition. This type of connectivity was introduced by Grigor'yan and Saloff-Coste in order to obtain stability results for Harnack inequalities and to study diffusions on manifolds with ends. As an application of our result, we obtain stability of the elliptic Harnack inequality under perturbations of the Dirichlet form with radial type weights.
