Self-similar energies on p.c.f. self-similar fractals

Abstract

On a large class of pcf (finitely ramified) self-similar fractals with possibly little symmetry we consider the question of existence and uniqueness of a Laplace operator. By considering positive refinement weights (local scaling factors) which are not necessarily equal we show that for each such fractal, under a certain condition, there are corresponding refinement weights which support a unique self-similar Dirichlet form. As compared to previous results, our technique allows us to replace symmetry by connectivity arguments.