Measurable sub-Riemannian geometry on the lifted Sierpinski gasket to the Heisenberg group

Abstract : 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.
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https://hal.inria.fr/hal-01927134
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Submitted on : Monday, November 19, 2018 - 4:19:42 PM
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  • HAL Id : hal-01927134, version 1

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Samia Haraketi, Ezedine Haouala, Antoine Lejay. Measurable sub-Riemannian geometry on the lifted Sierpinski gasket to the Heisenberg group. 2018. ⟨hal-01927134⟩

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