Geodesic Distances and Intrinsic Distances on Some Fractal Sets
Geodesic Distances and Intrinsic Distances on Some Fractal Sets
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DOI：
10.4171/prims/129
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发表时间：
2013-11
影响因子：
1.2
通讯作者：
M. Hino
中科院分区：
文献类型：
--
作者：
M. Hino
给定可度量化空间上的强局部Dirichlet型和$\mathbb{R}^N$-值函数，在此基础上引入测地距离和内蕴距离的概念.它们分别以几何和解析的方式定义，并且在某些经典情况下它们彼此密切相关。本文研究了当底层空间具有分形结构时，这些距离之间的关系。特别是，我们证明了他们的重合的一类自相似分形。
Given strong local Dirichlet forms and $\mathbb{R}^N$-valued functions on a metrizable space, we introduce the concepts of geodesic distance and intrinsic distance on the basis of these objects. They are defined in a geometric and an analytic way, respectively, and they are closely related with each other in some classical situations. In this paper, we study the relations of these distances when the underlying space has a fractal structure. In particular, we prove their coincidence for a class of self-similar fractals.