Id Photo
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: Mengminwei Building, Room 311-2, 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, function spaces on fractals...
  • Fractal geometry : self-similar sets; measures and dimensions; separating conditions...

  • Preprints

  • (with S. Cao) Equivalence of Besov spaces on p.c.f. self-similar sets, 29 pages. 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, 29 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 M.S. Hassler, R.S. Strichartz) Laplacians on Julia sets of rational maps, 15 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, 43 pages. pdf
  • (with S. Cao, H. Tian, L. Yang) Spectral decimation for a graph-directed fractal pair, 20 pages. pdf
  • (with S. Cao) Higher order Laplacians on fully symmetric p.c.f. fractals, 28 pages. pdf

  • Publications

  • (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 L. Mu, K. Yao, W. Su) Hausdorff dimension of the Weyl-Marchaud fractional derivative of a type of fractal functions, (in Chinese) Chinese Ann. Math. Ser. A 38 (2017), no. 3, 257-264.
  • (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

  • Teaching

  • Applied Mathematics, 2019-2020, 2nd semester.
  • Selected topics on analysis, 2019-2020, 2nd semester.

  • Useful links

    MathSciNet
    Arxiv

    Conferences

    7-th Cornell conference on analysis, probability, and mathematical physics on fractals
    Fractals and Related Fields IV(FARF4)

      last update: 2020.3


    Department of Mathematics, Nanjing University