Finite energy coordinates and vector analysis on fractals

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.

Cited by in corpus (5)

• Fractal snowflake domain diffusion with boundary and interior drifts
• Backward problems for stochastic differential equations on the Sierpinski gasket
• Canonical diffusions on the pattern spaces of aperiodic Delone sets
• Parabolic type equations associated with the Dirichlet form on the Sierpinski gasket
• Sobolev inequalities on product Sierpinski spaces