Dirichlet forms on unconstrained Sierpinski carpets

Abstract

We construct symmetric self-similar Dirichlet forms on unconstrained Sierpinski carpets, which are natural extension of planar Sierpinski carpets by allowing the small cells to live off the $1/k$ grids. The intersection of two cells can be a line segment of irrational length, and the non-diagonal assumption is dropped in this recurrent setting.

39 pages, 6 figures. We divide the old version into two parts. This updated version is the first part