Preprints

  • (with Q. Wang) Lq-spectra of box-like graph-directed self-affine measures: closed forms, with rotation, 54 pages. Sep. 12, 2023, pdf

  • (with S. Cao) Dirichlet forms on unconstrained Sierpinski carpets in $\mathbb{R}^3$, 44 pages. May 16, 2023, pdf

  • (with S. Cao, Y. Wang) Self-similar Dirichlet forms on polygon carpets, 42 pages.  May 26, 2022, pdf

  • (with S. Cao) Dirichlet forms on unconstrained Sierpinski carpets,  April, 2021 online, pdf (48 pages); Oct. 2021, version 2, pdf (72 pages); Since Jan 2023, divided into two parts: the existence part Jan. 2023, version 3, pdf (38 pages); the uniqueness and continuity part Sep. 2023, version 3, pdf (33 pages).








  • (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 Q. Gu) Boundary value problems for harmonic functions on domains in p.c.f. self-similar sets, 23 pages. pdf


  • Publications

  • (with S. Cao) Dirichlet forms on unconstrained Sierpinski carpets39 pages. pdf, to appear in Probab. Theory Related Fields


  • (with J.J. Cai, Y.Z. Wang) A uniform trace theorem for Dirichlet forms on Sierpinski fractalsJ. Funct. Anal. 286 (2024), no. 9, Paper No. 110367

    pdf, Journal

  • (with S. Cao) Equivalence of Besov spaces on p.c.f. self-similar sets29 pages. pdf, to appear in Canadian J. Math.

  • (with S. Cao) Brownian motion on the golden ratio Sierpinski gasket, 24 pages. pdf, to appear in Proc. Roy. Soc. Edinburgh Sect. A

  • (with Y. Deng, B. Li) Hausdorff and box dimension of self-affine set in non-Archimedean field, Nonlinearity 36 (2023), no. 7, 3483-3500.  pdf,  

  • (with Q. Gu, K.S. Lau, H.J. Ruan) Geodesic metrics on fractals and applications to heat kernel estimates,  Sci. China Math. 66 (2023), no. 5, 907-934. pdfJournal

  • (with Q. Gu, K.S. Lau) Homogeneous Dirichlet forms on p.c.f. fractals and their spectral asymptoticsPotential Anal. (2023)pdfJournal

  • (with S. Cao) A Sierpinski carpet like fractal without standard self-similar energy, Proc. Amer. Math. Soc. 151 (2023), no. 3, 1087-1102. pdfJournal

  • (with S. Cao, Q. Gu) p-energies on p.c.f. self-similar sets, Adv. Math., 405 (2022), Paper No. 108517. pdf, Journal


  • (with S. Cao) Sobolev spaces on p.c.f. self-similar sets II: boundary behavior and interpolation theorems, Forum Math. 34 (2022), no. 3, 749-779.  pdf, Journal

  • (with S. Cao, H. Tian, L. Yang) Spectral decimation for a graph-directed fractal pair, Sci. China Math., 65 (2022), no. 12, 2503-2520. pdf, Journal

  • (with S. Cao) Sobolev spaces on p.c.f. self-similar sets I: critical orders and atomic decompositions,  J. Funct. Anal. 282 (2022), no. 4, 109331. pdf, Journal

  • (with S. Cao, M.S. Hassler, E. Sandine, R.S. Strichartz) Existence and uniqueness of diffusions on the Julia sets of Misiurewicz-Sierpinski maps, Adv. Math. 389 (2021), 107922. pdf , Journal

  • (with S. Cao, Y. Huang, R.S. Strichartz, X. Zhu) Spectral analysis beyond l^2 on Sierpinski lattices, J. Fourier Anal. Appl. 27 (2021), no. 3, Paper No. 55. pdf , Journal

  • (with S. Cao) Higher order Laplacians on fully symmetric p.c.f. fractals, Studia Math. 257 (2021), no. 3, 313-345. pdf Journal

  • (with S. Cao) Resistance forms on self-similar sets with finite ramification of finite type, Potential Anal. (2021), 54, 581-606. 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) The Non-Degeneracy of Harmonic Structures on Planar 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, 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 type 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


  • Seminar

  • Fractal geometry (by Q. Wang), 2023-2024, 2rd semester, Thursday 13:30-16:30, Wujigeng Building, Room 305.

  • Probability on fractals (by B.-S. Wang), 2023-2024, 2rd semester, Thursday 09:30-11:30, Wujigeng Building, Room 305.

  • Analysis (by Y.-Z. Wang, H. Chen), 2023-2024, 2rd semester, Tuesday 13:30-16:30, Wujigeng Building, Room 305.

  • Selected topics on self-affine sets(by Q. Wang), 2023-2024, 1st semester, Thursday 13:30-16:30, Wujigeng Building, Room 305.

  • Analysis on fractals (by B.-S. Wang), 2023-2024, 1st semester, Thursday 09:00-11:30, Wujigeng Building, Room 305.

  • Analysis (by Y.-Z. Wang), 2023-2024, 1st semester, Monday 13:30-16:30, Wujigeng Building, Room 305.

  • Analysis on fractals and other metric spaces(by P.-D. Wang, B.-S. Wang), 2022-2023, 2nd semester, Thursday 09:00-11:30, Wujigeng Building, Room 305.

  • Selected topics on self-affine sets(by Q. Wang), 2022-2023, 2nd semester, Thursday 13:30-16:30, Wujigeng Building, Room 305.

  • Analysis on manifolds(by Y.-Z. Wang), 2022-2023, 2nd semester, Monday 13:30-16:30, Wujigeng Building, Room 209.

  • Fractal analysis, 2022-2023, 1st semester, Wednesday 13:30-14:30, Wujigeng Building, Room 305. (by P.-D. Wang)

  • Selected topics on fractal geometry, 2022-2023, 1st semester, Monday 13:30-14:30, Wujigeng Building, Room 305. (by H.-R. Tian, Q. Wang, S.-F. Wang)

  • Fractal geometry II, 2021-2022, 2nd semester, Wednesday 14:00-16:30, Wujigeng Building, Room 305.

  • Fractal analysis, 2021-2022, 2nd semester, Wednesday 09:30-12:00, Wujigeng Building, Room 305.

  • Fractal geometry I, 2021-2022, 2nd semester, Monday 14:00-17:00, Wujigeng Building, Room 305.

  • Selected topics on fractals, 2021-2022, 1st semester, Thursday 14:00-17:00, Wujigeng Building, Room 305.

  • Fractal analysis, 2021-2022, 1st semester, Thursday 09:30-12:00, Wujigeng Building, Room 305.

  • Fractal geometry, 2021-2022, 1st semester, Monday 14:00-17:00, Wujigeng Building, Room 305.

  • Fractal analysis, 2020-2021, 2nd semester, Tuesday 14:00-17:00, Wujigeng Building, Room 305.

  • Fractal geometry, 2020-2021, 2nd semester, Friday 09:00-12:00, Wujigeng Building, Room 305.

  • Analysis on graphs, 2020-2021, 2nd semester, Friday 14:00-17:00, Wujigeng Building, Room 305.

  • Fractal analysis, 2020-2021, 1st semester, Tuesday 13:00-16:00, Wujigeng Building, Room 305.

  • Fractal geometry, 2020-2021, 1st semester, Thursday 14:00-17:00, Wujigeng Building, Room 305.


  • Teaching

  • Analysis on graphs (reading seminar for freshmen, with Prof. Yalong Shi), 2023-2024, 2nd semester, Wednesday, 12:30-13:45, Wujigeng Building 305.

  • Selected topics on analysis, 2023-2024, 2nd semester, Monday, 14:00-16:00, Xian-II 103.

  • Calculus I, 2023-2024, 1st semester, Wednesday 10:10-12:00,14:00-15:50;Friday 08:00-09:50,NanJiao 102.

  • Fractal geometry, 2022-2023, 2nd semester, Friday, 14:00-16:50, Wujigeng Building 305.

  • Calculus I, 2022-2023, 1st semester, Tuesday 08:00-09:50;Friday 10:10-12:00,14:00-15:50,Guan-I 104.

  • Selected topics on analysis, 2021-2022, 2nd semester, Friday, 10:10-12:00, Xian-II 110.

  • Calculus I, 2021-2022, 1st semester, Wednesday 10:10-12:00,14:00-15:50;Friday 08:00-09:50,Yi-B 207.

  • Applied Mathematics, 2020-2021, 2nd semester, Tuesday 10:10-12:00; Thursday 08:00-09:50, Xian-II 211.


                 Online lession 1 (2021.3.2): 1.1群_概念.MP41.2群_例子.MP41.3群_性质.MP41.4群_同构.MP4


                 Online lession 2 (2021.3.4): 1.5群_变换群1.MP41.6群_变换群2.MP41.7群_置换群1.MP41.8群_置换群2.MP4


                 Online lession 3 (2021.3.9): 1.9群_循环群1.10群_子群1.11群_子群陪集1.MP41.12群_子群陪集2.MP4


                 Online lession 4 (2021.3.11): 1.13群_正规子群与商群1.MP41.14群_正规子群与商群2.MP41.15环.MP41.16域.MP4


  • Selected topics on analysis, 2020-2021, 2nd semester, Wednesday, 16:10-18:00, Jiao 103.


  • Calculus I, 2020-2021, 1st semester, Wednesday 10:10-12:00,14:00-15:50;Friday 10:10-12:00,Xian-II 212.

  • Applied Mathematics, 2019-2020, 2nd semester.

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

  • Selected topics on metric spaces: 


                 I,3.1距离空间定义与例子13.2距离空间定义与例子2.MP43.3距离空间定义与例子3.MP43.4距离空间定义与例子4.MP4


                II,3.5距离空间上的收敛.MP43.6距离空间上的点集.MP43.7距离空间上的映射.MP4


               III,3.8Lp空间的可分性.MP43.9连续函数空间的可分性.MP43.10有界函数空间的不可分性.MP4


               IV,3.11完备距离空间1.MP43.12完备距离空间2.MP43.13完备距离空间3.MP43.14完备距离空间4.MP43.15完备距离空间5.MP4


                V,3.16不动点定理1.MP43.17不动点定理2.MP4



  • Department of Mathematics, Nanjing University