Tootfinder

Conductive homogeneity of locally symmetric polygon-based self-similar sets
J. Kigami amd Y. Ota
https://arxiv.org/abs/2505.23057 https://

Conductive homogeneity of locally symmetric polygon-based self-similar sets
We provide a rich family of self-similar sets, called locally symmetric polygon-based self-similar sets, as examples of metric spaces having conductive homogeneity, which was introduced as a sufficient condition for the construction of counterparts of ``Sobolev spaces'' on compact metric spaces. In particular, our results imply the existence of ``Brownian motions'' on our family of self-similar sets at the same time. Unlike the known examples like the Sierpinski carpet by Barlow-Bass, unconstra…