Preprints
(with Q. Wang) The Hausdorff measure and uniform fibre conditions for Bara\'nski carpets, 40 pages. Nov. 25, 2024, pdf
(with Q. Wang, S.-F. Wang) Assouad and lower dimensions of graph-directed Bedford-McMullen carpets, 24 pages. Nov. 23, 2024, pdf
(with S. Cao) 分形上的能量型（Energies on fractals）, 20 pages. Sep. 5, 2024, pdf
(with Q. Wang) Lq-spectra of box-like graph-directed self-affine measures: closed forms, with rotation, 56 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) 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) BGD domains in p.c.f. self-similar sets I: boundary value problems for harmonic functions, 27 pages. pdf
Publications
(with S. Cao, Y.-Z. Wang) Self-similar Dirichlet forms on polygon carpets, 42 pages, to appear in J. Anal. Math. (2025). pdf
(with Q. Wang, S.-F. Wang) Lq-spectra of graph-directed planar non-conformal measures, Nonlinearity 37 (2024), 095003 (25pp). pdf, Journal
(with S. Cao) Dirichlet forms on unconstrained Sierpinski carpets, Probab. Theory Related Fields 189 (2024), no. 1-2, 613-657. pdf, Journal
(with J.-J. Cai, Y.-Z. Wang) A uniform trace theorem for Dirichlet forms on Sierpinski fractals, J. Funct. Anal. 286 (2024), no. 9, Paper No. 110367.
(with S. Cao) Equivalence of Besov spaces on p.c.f. self-similar sets, Canad. J. Math. 76 (2024), no. 4, 1109-1143. pdf, Journal
(with S. Cao) Brownian motion on the golden ratio Sierpinski gasket, Proc. Roy. Soc. Edinburgh Sect. A 154 (2024), no. 3, 699-726. pdf, Journal
(with Q. Gu, K.-S. Lau) Homogeneous Dirichlet forms on p.c.f. fractals and their spectral asymptotics, Potential Anal. 60 (2024), no. 1, 219-252. pdf, Journal
(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, Journal
(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. pdf, Journal
(with S. Cao) A Sierpinski carpet like fractal without standard self-similar energy, Proc. Amer. Math. Soc. 151 (2023), no. 3, 1087-1102. pdf, Journal
(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.-R. Tian, L.-J. 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.-R. 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.
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 T.-Y. Hu, S.-H. Yao), 2024-2025, 2rd semester, Wednesday 13:30-16:30, Wujigeng Building, Room 305.
Probability on fractals (by B.-S. Wang), 2024-2025, 2rd semester, Wednesday 09:30-11:30, Wujigeng Building, Room 305.
Analysis and probability on graphs (by P.-D. Wang, H.-P. Jiao), 2024-2025, 2rd semester, Monday 13:30-16:30, Wujigeng Building, Room 305.
Analysis and probability on fractals (by B.-S. Wang), 2024-2025, 1st semester, Monday 09:00-11:30, Wujigeng Building, Room 305.
Fractal geometry (by T.-Y. Hu, S.-H. Yao), 2024-2025, 1st semester, Monday 13:30-16:30, Wujigeng Building, Room 305.
Analysis and probability on graphs (by P.-D. Wang, H.-P. Jiao), 2024-2025, 1st semester, Friday 13:30-16:30, Wujigeng Building, Room 305.
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
Selected topics on analysis, 2024-2025, 2nd semester, Monday, 14:00-16:00, Xian-II 104.
Calculus I, 2024-2025, 1st semester, Tuesday 14:00-15:50；Thursday 10:10-12:00，14:00-15:50, Guan-I 407.
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.MP4, 1.2群_例子.MP4, 1.3群_性质.MP4, 1.4群_同构.MP4
Online lession 2 (2021.3.4): 1.5群_变换群1.MP4, 1.6群_变换群2.MP4, 1.7群_置换群1.MP4, 1.8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.MP4, 1.12群_子群陪集2.MP4
Online lession 4 (2021.3.11): 1.13群_正规子群与商群1.MP4, 1.14群_正规子群与商群2.MP4, 1.15环.MP4, 1.16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1, 3.2距离空间定义与例子2.MP4, 3.3距离空间定义与例子3.MP4, 3.4距离空间定义与例子4.MP4
II，3.5距离空间上的收敛.MP4, 3.6距离空间上的点集.MP4, 3.7距离空间上的映射.MP4
III，3.8Lp空间的可分性.MP4, 3.9连续函数空间的可分性.MP4, 3.10有界函数空间的不可分性.MP4
IV，3.11完备距离空间1.MP4, 3.12完备距离空间2.MP4, 3.13完备距离空间3.MP4, 3.14完备距离空间4.MP4, 3.15完备距离空间5.MP4
V，3.16不动点定理1.MP4, 3.17不动点定理2.MP4