Arxiv Preprints
Arxiv Preprints
25. Uniform boundary Harnack principle for non-local operators on metric measure spaces
Shiping Cao and Zhen-Qing Chen, arXiv:2410.20719.
24. Boundary trace theorems for symmetric reflected diffusions
Shiping Cao and Zhen-Qing Chen, arXiv:2410.19201.
23. Uniqueness and convergence of resistance forms on unconstrained Sierpinski carpets
Shiping Cao and Hua Qiu, arXiv:2402.01949.
22. Convergence of resistances on generalized Sierpiński carpets
Shiping Cao and Zhen-Qing Chen, arXiv:2402.01949.
21. Dirichlet forms on unconstrained Sierpinski carpets in $\mathbb{R}^3$,
Shiping Cao and Hua Qiu, arXiv:2305.09292.
20. Self-similar Dirichlet forms on polygon carpets,
Shiping Cao, Hua Qiu and Yizhou Wang, to appear in J. Anal. Math.
19. Whether $p$-conductive homogeneity holds depends on $p$.
Shiping Cao and Zhen-Qing Chen, to appear in J. Fractal Geom.
18. On Kigami’s conjecture of the embeddings $\mathcal{W}^p(K)\subset C(K)$
Shiping Cao, Zhen-Qing Chen and Kumagai Takashi, Proc. Amer. Math. Soc. 152 (2024), no. 8, 3393--3402.
17. Dirichlet forms on unconstrained Sierpinski carpets,
Shiping Cao and Hua Qiu, Probab. Theory Related Fields 189 (2024) 613–657.613–657
16. Brownian motion on the golden ratio Sierpinski gasket,
Shiping Cao and Hua Qiu, Proc. Roy. Soc. Edinburgh Sect. A 154 (2024), no. 3, 699–726.
15. Equivalence of Besov spaces on p.c.f. self-similar sets,
Shiping Cao and Hua Qiu, Canad. J. Math. 76 (2024), no. 4, 1109--1143.
Shiping Cao, Adv. Math. 435 (2023), Paper No. 109382, 38 pp.
13. Convergence of energy forms on Sierpinski gaskets with added rotated triangle,
Shiping Cao, Potential Anal. 59 (2023), no. 4, 1793–1825.
12. p-energies on p.c.f. self-similar sets,
Shiping Cao, Qingsong Gu and Hua Qiu, Adv. Math. 405 (2022), Paper No. 108517, 58 pp.
11. A Sierpinski carpet like fractal without standard self-similar energy
Shiping Cao and Hua Qiu, Proc. Amer. Math. Soc. 151 (2023), no. 3, 1087-1102.
10. Sobolev spaces on p.c.f. self-similar sets II: boundary behavior and interpolation theorems,
Shiping Cao and Hua Qiu, Forum Math. 34 (2022), no. 3, 749–779.
9. Sobolev spaces on p.c.f. self-similar sets I: critical orders and atomic decompositions,
Shiping Cao and Hua Qiu, J. Funct. Anal. 282 (2022), no. 4, Paper No. 109331, 47 pp.
8. Existence and uniqueness of diffusions on the Julia sets of Misiurewicz-Sierpinski maps,
Shiping Cao, Malte S. Hassler, Hua Qiu, Ely Sandine and Robert S. Strichartz, Adv. Math., 389 (2021), Paper No. 107922, 41 pp.
7. Spectral analysis beyond $\ell^2$ on Sierpinski lattices,
Shiping Cao, Yiqi Huang, Hua Qiu, Robert S. Strichartz and Xiaohan Zhu, J. Fourier Anal. Appl. 27 (2021), no. 3, Paper No. 55, 19 pp.
6. Resistance forms on self-similar sets with finite ramification of finite type,
Shiping Cao and Hua Qiu, Potential Anal. 54 (2021) 581-606.
5. Higher order Laplacians on p.c.f. fractals with three boundary points and dihedral symmetry,
Shiping Cao and Hua Qiu, Studia Math. 257 (2021), 313-345.
4. A trace theorem for Sobolev spaces on the Sierpinski gasket,
Shiping Cao, Shuangping Li, Robert S. Strichartz and Prem A. Talwai, Commun. Pure Appl. Anal. 19 (2020) 3901-3916
3. The Mathieu differential equation and generalizations to infinite fractafolds,
Shiping Cao, Anthony Coniglio, Xueyan Niu, Richard Rand and Robert S. Strichartz, Commun. Pure Appl. Anal. 19 (2020), 1795-1845.
2. Boundary value problems for harmonic functions on domains in Sierpinski gaskets,
Shiping Cao and Hua Qiu, Commun. Pure Appl. Anal. 19 (2020), 1147-1179.
Shiping Cao and Hua Qiu, Constr. Approx. 46 (2017), 319-347.