Self-similar energies on post-critically finite self-similar fractals

Journal article

On a large class of post-critically finite (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 with previous results, our technique allows us to replace symmetry by connectivity arguments. © 2006 London Mathematical Society.

Authors: Hambly, B; Metz, V; Teplyaev, A

• Publication status: Published
• Journal: JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES
• Volume: 74
• Issue: 1
• Pages: 93-112
• Publication date: 2006-08-01
• DOI: 10.1112/S002461070602312X
• EISSN: 1469-7750
• ISSN: 0024-6107
• Language: English