Measurable sub-Riemannian geometry on the lifted Sierpinski gasket to the Heisenberg group
Résumé
We construct a lift of the Sierpinski gasket to the Heisenberg group, the invariant set of a horizontal iterated functions system. As we have a post critically finite self-similar set, using analytic approach, we define a local regular Dirichlet form. By using the theory of Dirichlet forms, we have a diffusion process and a Laplacian which we have defines as being the limit of discrete Laplacians on a sequence of finite graphs which approximate this set.
Domaines
Probabilités [math.PR]
Origine : Fichiers produits par l'(les) auteur(s)
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