Homepage of Prof. Hua Qiu

Hua Qiu: Department of Mathematics
Nanjing University
Hankou Road, No.22, Goulou District
210093, Nanjing
P.R. China

I am a Professor of Mathematics at Nanjing University.

Contact information

Office: Wujigeng Building, Room 309, Gulou Campus, Nanjing University

Email: huaqiu(at)nju.edu.cn

Education and appointment

2007.6: Ph.D. in Mathematics, Nanjing University

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

Research interests

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...

Preprints

(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) Translation invariant Dirichlet forms and their spectral asymptotics on p.c.f. fractals, 27 pages, in preparation. version 1 on Jan. 1, 2020, 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, 13 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, to appear in Studia Math. pdf

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

(with X. Fu and J.P. Gabardo) Open set condition and pseudo Hausdorff measure of self-affine IFSs, to appear in Nonlinearity. pdf

(with S. Cao) A topological proof of the non-degeneracy of harmonic structures on Sierpinski gaskets, to appear in Anal. Theory Appl.pdf

(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, Fractals 27 (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. Systems 35 (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. Systems 32 (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, Fractals 15 (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 Fractals 33 (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 Fractals 28 (2006), no. 4, 958-965. Journal