4 citations · 20 across the 27 of their papers we have counts for
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-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…
Eigenvalues of Laplacians on Higher Dimensional Vicsek Set Graphs
Shiping Cao, Robert S. Strichartz, Melissa Wei
We study the graphs associated with Vicsek sets in higher dimensional settings. First, we study the eigenvalues of the Laplacians on the approximating graphs of the Vicsek sets, fi…
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…