Article ID Journal Published Year Pages File Type
4666061 Advances in Mathematics 2013 36 Pages PDF
Abstract

We provide a definition of the integral, along paths in the Sierpinski gasket KK, for differential smooth 1-forms associated to the standard Dirichlet form EE on KK. We show how this tool can be used to study the potential theory on KK. In particular, we prove: (i) a de Rham reconstruction of a 1-form from its periods around lacunas in KK; (ii) a Hodge decomposition of 1-forms with respect to the Hilbertian energy norm; (iii) the existence of potentials of smooth 1-forms on a suitable covering space of KK. We finally show that this framework provides versions of the de Rham duality theorem for the fractal KK.

Keywords
Related Topics
Physical Sciences and Engineering Mathematics Mathematics (General)
Authors
, , , ,