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.
Document type :
Preprints, Working Papers, ...
Complete list of metadatas

Cited literature [33 references]  Display  Hide  Download

https://hal.inria.fr/hal-01927134
Contributor : Antoine Lejay <>
Submitted on : Monday, November 19, 2018 - 4:19:42 PM
Last modification on : Sunday, June 2, 2019 - 10:00:02 AM
Long-term archiving on : Wednesday, February 20, 2019 - 3:47:32 PM

File

article_sierpinski_horizontal....
Files produced by the author(s)

Identifiers

  • HAL Id : hal-01927134, version 1

Citation

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

Share

Metrics

Record views

77

Files downloads

70