My research field is analysis on fractals and metric measure spaces.
Publications
Gradient Estimate for the Heat Kernel on Some Fractal-Like Cable Systems and Quasi-Riesz Transforms (with Baptiste Devyver and Emmanuel Russ), International Mathematics Research Notices, Volume 2023, Issue 18, September 2023, Pages 15537–15583. Journal link, arXiv link.
On the domains of Dirichlet forms on metric measure spaces, Mathematische Zeitschrift, 2022, 301(2), 2129-2154. Journal link, arXiv link.
Metrics and Uniform Harnack Inequality on the Strichartz Hexacarpet, Advances in Analysis and Geometry 3, de Gruyter, 2021, 275-296. Journal link, arXiv link.
Local and Non-Local Dirichlet Forms on the Sierpi\'nski Carpet (with Alexander Grigor’yan), Transactions of the American Mathematical Society, 2019, 372(6), 3985-4030. Journal link, arXiv link.
Determination of the walk dimension of the Sierpi\'nski gasket without using diffusion (with Alexander Grigor’yan), Journal of Fractal Geometry, 2018, 5(4), 419-460. Journal link, arXiv link.
Equivalent Semi-Norms of Non-Local Dirichlet Forms on the Sierpi\'nski Gasket and Applications, Potential Analysis, 2018, 49(2), 287-308. Journal link, arXiv link.
Heat Kernel Estimates on Julia Sets, Acta Mathematica Scientia, 2017, 37B(5): 1399-1414. Journal link.
Preprints
On the dichotomy of $p$-walk dimensions on metric measure spaces, preprint. arXiv link.
Energy inequalities for cutoff functions of $p$-energies on metric measures spaces, preprint. arXiv link.
On singularity of $p$-energy measures on metric measure spaces, preprint. arXiv link.
Korevaar-Schoen and heat kernel characterizations of Sobolev and BV spaces on local trees (with Fabrice Baudoin and Li Chen), preprint. arXiv link.
A direct proof of the cutoff Sobolev inequality on the Sierpi\'nski gasket, preprint. arXiv link.
$p$-Poincar\'e inequalities and cutoff Sobolev inequalities on metric measure spaces, preprint. arXiv link.
H\"older regularity of harmonic functions on metric measure spaces (with Jin Gao), preprint. arXiv link.
Korevaar-Schoen spaces on Sierpi\'nski carpets, preprint. arXiv link.
Construction of Local Regular Dirichlet Form on the Sierpi\'nski Gasket using $\Gamma$-Convergence, preprint. arXiv link.