快速数量增长和容量估计的几何影响
Geometric implications of fast volume growth and capacity estimates
摘要：
我们得到了体积加倍度量测度Dirichlet空间的环的连通性，该空间满足Poincaré不等式、容量估计和体积快速增长条件。这种类型的连通性是由Grigor'yan和Saloff-Coste引入的，目的是为了获得Harnack不等式的稳定性结果，并研究具有端点的流形上的扩散。作为结果的一个应用，我们得到了椭圆型Harnack不等式在Dirichlet型扰动下的稳定性。
英文摘要：
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.
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