Finite energy coordinates and vector analysis on fractals
Probability
2018-06-29 v1 Mathematical Physics
Differential Geometry
Functional Analysis
Metric Geometry
math.MP
Abstract
We consider (locally) energy finite coordinates associated with a strongly local regular Dirichlet form on a metric measure space. We give coordinate formulas for substitutes of tangent spaces, for gradient and divergence operators and for the infinitesimal generator. As examples we discuss Euclidean spaces, Riemannian local charts, domains on the Heisenberg group and the measurable Riemannian geometry on the Sierpinski gasket.
Cite
@article{arxiv.1501.04541,
title = {Finite energy coordinates and vector analysis on fractals},
author = {Michael Hinz and Alexander Teplyaev},
journal= {arXiv preprint arXiv:1501.04541},
year = {2018}
}