Given strong local Dirichlet forms and -valued functions on a metrizable space, we introduce the concepts of geodesic distance and intrinsic distance on the basis of these objects. They are dened in a geometric and an analytic way, respectively, and they are closely related to 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.
Cite this article
Masanori Hino, Geodesic Distances and Intrinsic Distances on Some Fractal Sets. Publ. Res. Inst. Math. Sci. 50 (2014), no. 2, pp. 181–205DOI 10.4171/PRIMS/129