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

• Autores: Ben M. Hambly, V. Metz, Alexander Teplyaev
• Localización: Journal of the London Mathematical Society, ISSN 0024-6107, Vol. 74, Nº 1, 2006, págs. 93-112
• Idioma: inglés
• DOI: 10.1112/s002461070602312x
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• Resumen

  • 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.