Some properties of energy measures on Sierpinski gasket type fractals

TL;DR

This paper investigates the distribution of energy measures for harmonic functions on the Sierpinski gasket, confirming a part of a conjecture within a broader theoretical framework.

Contribution

It extends previous work by confirming a conjecture about energy measure distribution on the Sierpinski gasket in a more general setting.

Findings

Confirmed part of the conjecture on energy measures

Extended the theoretical framework for energy measures

Provided new insights into harmonic functions on fractals

Abstract

We confirm, in a more general framework, a part of the conjecture posed by R. Bell, C.-W. Ho, and R. S. Strichartz [Energy measures of harmonic functions on the Sierpi\'nski gasket, Indiana Univ. Math. J. 63 (2014), 831--868] on the distribution of energy measures for the canonical Dirichlet form on the two-dimensional standard Sierpinski gasket.