教育经历

2007.6: Ph.D. in Mathematics, Nanjing University

工作经历

2018.12--: Professor, Department of Mathematics, Nanjing University

研究兴趣

• Fractal Analysis: Laplacians and Dirichlet forms, spectral asymptotical analysis, heat kernel estimates, function spaces on fractals...

• Fractal geometry: self-similar sets; measures and dimensions; separating conditions...

学术兼职

学术奖励

论文

Preprints

• (with S. Cao) Dirichlet forms on unconstrained Sierpinski carpets, 48 pages. pdf

  
  

• (with S. Cao) Brownian motion on the golden ratio Sierpinski gasket, 22 pages. version 1 on September 16, 2020, pdf

• (with S. Cao, M.S. Hassler, E. Sandine, R.S. Strichartz) Existence and uniqueness of diffusions on the Julia sets of Misiurewicz-Sierpinski maps, 31 pages. version 1 on August 11, 2020, pdf

  
  

• (with S. Cao) Function spaces on p.c.f. self-similar sets III: embedding and interpolation theorems, 58 pages, in preparation. version 1 on Feb.22, 2020, pdf

• (with S. Cao) Sobolev spaces on p.c.f. self-similar sets II: boundary behavior and interpolation theorems, 31 pages. pdf

• (with S. Cao) Sobolev spaces on p.c.f. self-similar sets I: critical orders and atomic decompositions, 39 pages. pdf

• (with Q. Gu) Harmonic measures of domains in nested fractals, 18 pages. 

  pdf

  
  

• (with Q. Gu, K.S. Lau) Atypical Dirichlet forms on p.c.f. fractals and their spectral asymptotics, 32 pages. pdf

  
  

• (with S. Cao) Equivalence of Besov spaces on p.c.f. self-similar sets, 29 pages.pdf

• (with S. Cao, Y. Huang, R.S. Strichartz, X. Zhu) Spectral analysis beyond l^2 on Sierpinski lattices, 17 pages. pdf

  
  

• (with Q. Gu, K.S. Lau, H.J. Ruan) Metrics on fractals and sub-Gaussian heat kernel estimates, 37 pages. pdf

• (with S. Cao, H. Tian, L. Yang) Spectral decimation for a graph-directed fractal pair, 20 pages. pdf




Publications

• (with S. Cao) Higher order Laplacians on fully symmetric p.c.f. fractals, Studia Math. pdf , Journal

• (with S. Cao) Resistance forms on self-similar sets with finite ramification of finite type, Potential Anal. pdf , Journal 

• (with X. Fu and J.P. Gabardo) Open set condition and pseudo Hausdorff measure of self-affine IFSs, Nonlinearity.33 (2020), no. 6, 2592-2614. pdf , Journal

• (with S. Cao) A topological proof of the non-degeneracy of harmonic structures on Sierpinski gaskets, Anal. Theory Appl., 36 (2020), 510-516. pdf , Journal

• (with S. Cao) Boundary value problems for harmonic functions on domains in Sierpinski gaskets, Commun. Pure Appl. Anal.19 (2020), no. 2, 1147-1179. pdf , Journal

• (with H. Tian) Restrictions of Laplacian eigenfunctions to edges in the Sierpinski gasket, Constr. Approx.50 (2019), no. 2, 243-269. pdf , Journal

• (with Y. Li) Fractal sets in the field of p-adic analogue of the complex numbers, Fractals27 (2019), no. 4, 1950053. pdf , Journal

• Exact spectrum of the Laplacian on a domain in the Sierpinski gasket, J. Funct. Anal.277 (2019), no. 3, 806-888. pdf , Journal

• (with Y. Wu, K. Yao) Mean value property of harmonic functions on the tetrahedral Sierpinski gasket, J. Fourier Anal. Appl.25 (2019), no. 3, 785-803. pdf , Journal

• (with Q. Gu, K.S. Lau) On a recursive construction of Dirichlet form on the Sierpinski gasket, J. Math. Anal. Appl.474 (2019), no. 1, 674-692. pdf , Journal

• (with S. Cao) Some properties of the derivatives on Sierpinski gasket tyoe fractals, Constr. Approx.46 (2017), no. 2, 319-347. pdf , Journal

• (with D. Dou, M. Fan) Topological entropy on subsets for fixed-point free flows, Discrete Contin. Dyn. Syst.37 (2017), no. 12, 6319-6331. pdf , Journal

• (with Y. Li) p-adic Laplacian in local fields, Nonlinear Anal.139 (2016), 131-151. pdf , Journal

• Exact Hausdorff and packing measures of Cantor sets with overlaps, Ergodic Theory Dynam. Systems35 (2015), no. 8, 2632-2668. pdf , Journal

• (with Z. Guo, R. Kogan, R.S. Strichartz) Boundary value problems for a family of domains in the Sierpinski gasket, Illinois J. Math.58 (2014), no. 2, 497-519. pdf , Journal

• (with R.S. Strichartz) Mean value properties of harmonic functions on Sierpinski gasket type fractals, J. Fourier Anal. Appl.19 (2013), no. 5, 943-966. 

  pdf , Journal

• Continuity of packing measure functions of self-similar iterated function systems, Ergodic Theory Dynam. Systems32 (2012), no. 3, 1101-1115. pdf , Journal

• Gibbs-Butzer derivatives over p-adic fields, Appl. Anal.90 (2011), no. 3-4, 545-561. Journal

• (with W. Su) Distributional dimension of fractal sets in local fields, Acta Math. Sin.(Engl. Ser.)24 (2008), no. 1, 147-158. Journal

• (with W. Su) The connection between the orders of p-adic calculus and the dimensions of the Weierstrass type function in local fields, Fractals15 (2007), no. 3, 279-287. Journal

• (with Y. Li, W. Su) On Hausdorff dimension of certain Riesz product in local fields, Anal. Theory Appl.23 (2007), no. 2, 147-161. Journal

• (with W. Su) 3-adic Cantor function on local fields and its p-adic derivative, Chaos Solitons Fractals33 (2007), no. 5, 1625-1634. Journal

• (with W. Su) Measures and dimensions of fractal sets in local fields, Progr. Natur. Sci (English Ed.)16 (2006), no. 12, 1260-1268. Journal

• (with W. Su) Weierstrass-like functions on local fields and their p-adic derivatives, Chaos Solitons Fractals28 (2006), no. 4, 958-965. Journal

  
  

其他