7 citations · 38 across the 29 of their papers we have counts for
29 papers
Dirichlet forms on unconstrained Sierpinski carpets in
Shiping Cao, Hua Qiu
We prove the existence of a strongly local, regular, self-similar Dirichlet form with a sub-Gaussian heat kernel estimate on an unconstrained Sierpinski carpet in . I…
Hausdorff and box dimension of self-affine set in non-Archimedean field
Yang Deng, Bing Li, Hua Qiu
In this paper we consider affine iterated function systems in locally compact non-Archimedean field . We establish the theory of singular value composition in $\mathbb{…
Self-similar Dirichlet forms on polygon carpets
Shiping Cao, Hua Qiu, Yizhou Wang
We construct symmetric self-similar diffusions with sub-Gaussian heat kernel estimates on two types of polygon carpets, which are natural generalizations of planner Sierpinski carp…
-energies on p.c.f. self-similar sets
Shiping Cao, Qingsong Gu, Hua Qiu
We study -energies on post critically finite (p.c.f.) self-similar sets for , as limits of discrete -energies on approximation graphs, extending the construction…
A Sierpinski carpet like fractal without standard self-similar energy
Shiping Cao, Hua Qiu
We construct a Sierpinski carpet like fractal, on which a self-similar diffusion with sub-Gaussian heat kernel estimate does not exist, in contrast to previous researches on the ex…
Dirichlet forms on unconstrained Sierpinski carpets
Shiping Cao, Hua Qiu
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 liv…