华波波 - 复旦大学 - 数学科学学院

个人简介

华波波，复旦大学数学科学学院教授，从事几何分析、偏微分方程、离散几何分析等研究。 2010年在复旦大学获理学博士学位，其后在德国Max Planck Institute for Mathematics in the Sciences从事博士后研究，2014年至今任职于复旦大学数学科学学院。代表性工作系统发展了离散几何分析理论，包括离散调和函数、热方程、Ricci流等。至今在Amer. J. Math., J. Reine Angew. Math., Geom. Topol., Math. Ann.等数学期刊上共发表论文60余篇。 2015年入选国家高层次青年人才项目、2019年入选国家高层次人才项目。教育经历 Max Planck Institute for Mathematics in the Sciences Postdoc Apr. 2011-Jan. 2014 Courant Institute of Mathematical Sciences Visiting student Feb. 2009-Feb. 2010 Fudan University 博士学位 2005-2010 Shanghai Jiaotong University 学士学位 2001-2005 工作经历 Fudan University School of Mathematical Sciences Professor Dec. 2019-now Fudan University School of Mathematical Sciences Associate Professor Feb. 2014-Nov. 2019

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B.H. and Wendi Xu, Existence of ground state solutions to some nonlinear Schr?dinger equations on lattice graphs. Calc. Var. Partial Differential Equations 62 (2023), no. 4, Paper No. 127, 17 pp. B.H., Ruowei Li and Lidan Wang, A class of semilinear elliptic equations on groups of polynomial growth. J. Differential Equations 363 (2023), 327–349. B.H., Yong Lin and Yanhui Su, Payne-Polya-Weinberger, Hile-Protter and Yang's inequalities for Dirichlet Laplace eigenvalues on integer lattices. J. Geom. Anal. 33 (2023), no. 7, Paper No. 217, 23 pp. B.H., Matthias Keller, Michael Schwarz and Melchior Wirth, Sobolev-type inequalities and eigenvalue growth on graphs with finite measure. Proc. Amer. Math. Soc. 151 (2023), no. 8, 3401–3414. Yohji Akama and B.H., Hyperbolic polyhedral surfaces with regular faces. Discrete Math. 346 (2023), no. 1, Paper No. 113213, 16 pp. Ke Feng, Huabin Ge and B.H., Combinatorial Ricci flows and the hyperbolization of a class of compact 3-manifolds. Geom. Topol. 26 (2022), no. 3, 1349–1384. B.H. and Yanhui Su, Total curvature of planar graphs with nonnegative combinatorial curvature. Trans. Amer. Math. Soc. 375 (2022), no. 12, 8423–8444. B.H., Yan Huang and Zuoqin Wang, Cheeger estimates of Dirichlet-to-Neumann operators on infinite subgraphs of graphs. J. Spectr. Theory 12 (2022), no. 3, 1079–1108. B.H., Dimensional bounds for ancient caloric functions on graphs. Int. Math. Res. Not. IMRN 2022, no. 6, 4022–4039. Ke Feng, Huabin Ge, B.H. and Xu Xu, Combinatorial Ricci flows with applications to the hyperbolization of cusped 3-manifolds. Int. Math. Res. Not. IMRN 2022, no. 20, 15549–15573. Zunwu He and B.H., Harmonic functions of polynomial growth on infinite penny graphs. J. Lond. Math. Soc. (2) 105 (2022), no. 1, 565–586. Zunwu He and B.H., Upper bounds for the Steklov eigenvalues on trees. Calc. Var. Partial Differential Equations 61 (2022), no. 3, Paper No. 101, 15 pp. B.H. and Jia-Yong Wu, Gap theorems for ends of smooth metric measure spaces. Proc. Amer. Math. Soc. 150 (2022), no. 11, 4947–4957. B.H., Matthias Keller, Daniel Lenz, Marcel Schmidt, On Lp Liouville theorems for Dirichlet forms. Dirichlet forms and related topics, 201–221, Springer Proc. Math. Stat., 394, Springer, Singapore, [2022], ?2022. Huabin Ge, B.H. and Zhou, Ze; Circle patterns on surfaces of finite topological type. Amer. J. Math. 143 (2021), no. 5, 1397–1430. Yohji Akama, B.H., Yanhui Su and Lili Wang, A curvature notion for planar graphs stable under planar duality. Adv. Math. 385 (2021), Paper No. 107731, 44 pp. Huabin Ge, B.H. and Ze Zhou, Combinatorial Ricci flows for ideal circle patterns. Adv. Math. 383 (2021), Paper No. 107698, 26 pp. B.H., Ancient caloric functions on graphs with unbounded Laplacians. Int. Math. Res. Not. IMRN 2021, no. 4, 3056–3077. B.H. and Ruowei Li, The existence of extremal functions for discrete Sobolev inequalities on lattice graphs. J. Differential Equations 305 (2021), 224–241. B.H., Jun Masamune, Rados?aw K. Wojciechowski, Essential self-adjointness and the L2-Liouville property. J. Fourier Anal. Appl. 27 (2021), no. 2, Paper No. 26, 27 pp. Fengwen Han, B.H. and Lili Wang, Time analyticity of solutions to the heat equation on graphs. Proc. Amer. Math. Soc. 149 (2021), no. 6, 2279–2290. Huabin Ge, B.H. and Wenfeng Jiang, The limit of first eigenfunctions of the p-Laplacian on graphs. Pacific J. Math. 312 (2021), no. 1, 103–112. B.H., Discrete harmonic functions on infinite penny graphs. Vietnam J. Math. 49 (2021), no. 2, 461–472. Huabin Ge and B.H., 3-dimensional combinatorial Yamabe flow in hyperbolic background geometry. Trans. Amer. Math. Soc. 373 (2020), no. 7, 5111–5140. B.H. and Lili Wang, Dirichlet p-Laplacian eigenvalues and Cheeger constants on symmetric graphs. Adv. Math. 364 (2020), 106997, 34 pp. B.H. and Yanhui Su, The first gap for total curvatures of planar graphs with nonnegative curvature. J. Graph Theory 93 (2020), no. 3, 395–439. Li Chen, Thierry Coulhon and B.H., Riesz transforms for bounded Laplacians on graphs. Math. Z. 294 (2020), no. 1-2, 397–417. B.H. and Yanhui Su, The set of vertices with positive curvature in a planar graph with nonnegative curvature, Adv. Math. 343 (2019), 789–820. B.H. and Florentin Münch, Rados?aw K. Wojciechowski, Coverings and the heat equation on graphs: stochastic incompleteness, the Feller property, and uniform transience. Trans. Amer. Math. Soc. 372 (2019), no. 7, 5123–5151. B.H. and Yong Lin, Graphs with large girth and nonnegative curvature dimension condition. Comm. Anal. Geom. 27 (2019), no. 3, 619–638. B.H., Liouville theorem for bounded harmonic functions on manifolds and graphs satisfying non-negative curvature dimension condition. Calc. Var. Partial Differential Equations 58 (2019), no. 2, Paper No. 42, 8 pp. Huabin Ge and B.H., On combinatorial Calabi flow with hyperbolic circle patterns, Adv. Math., 333: 523–538, 2018. B.H. and Luo Xin, Davies-Gaffney-Grigor’yan lemma on simplicial complexes, Math. Z. 290(2018), no. 3-4, 1041-1053. Huabin Ge, B.H. and Wenfeng Jiang, A note on Liouville type equations on graphs, Proc. Amer. Math. Soc. 146 (2018), 4837–4842. B.H. and Yan Huang, Neumann Cheeger constants on graphs. J. Geom. Anal. 28 (2018), no. 3, 2166–2184. Frank Bauer, B.H. and Shing-Tung Yau. Sharp Davies-Gaffney-Grigor’yan lemma on graphs, Math. Ann. 368(3-4): 1429–1437, 2017. B.H. and Yong Lin, Stochastic completeness for graphs with curvature dimension conditions, Adv. Math., 306, 279–302, 2017. B.H., Yan Huang and Zuoqin Wang, First eigenvalue estimates of Dirichlet-to-Neumann operators on graphs, Calc. Var. Partial Differential Equations, 56:178, 2017. B.H., Shiping Liu and Chao Xia. Liouville theorems for f-harmonic maps into Hadamard spaces, Pacific Journal of Mathematics, 290, no. 2, 381–402, 2017. arXiv:1305.0485. B.H. and Yong Lin, Curvature notions on graphs, Frontiers of Mathematics in China 11, no. 5, 1275–1290, 2016. Fatihcan Atay and B.H., On the symmetry of the Laplacian spectra of signed graphs, Linear Algebra Appl. 495, 24-37, 2016. arXiv:1411.6113. Frank Bauer, B.H., Juergen Jost, Shiping Liu and Guofang Wang, The geometric meaning of curvature. Local and nonlocal aspects of Ricci curvature, Lecture Notes in Mathematics, no. 2184, Modern Approaches to Discrete Curvature, 1–62, edited by L. Najman and P. Romon. B.H., Juergen Jost and Shiping Liu. Geometric analysis aspects of infinite semiplanar graphs with nonnegative curvature, J. Reine Angew. Math., 700, 1–36, 2015, arXiv:1107.2826. B.H. and Juergen Jost. Geometric analysis aspects of infinite semiplanar graphs with nonnegative curvature II, Trans. Amer. Math. Soc., 367, 2509-2526, 2015, arXiv:1112.6282. B.H. and Delio Mugnolo, Time regularity and long-time behavior of parabolic p-Laplace equations on infinite graphs, J. Differential Equations 259, no. 11, 6162–6190, 2015. arXiv:1410.1584. B.H. and Juergen Jost. Polynomial growth harmonic functions on groups of polynomial volume growth, Math. Z., 280, no. 1-2, 551–567, 2015. arXiv:1201.5238. Frank Bauer, B.H. and Shing-Tung Yau. Davies-Gaffney-Grigor’yan lemma on graphs, Comm. Anal. Geom. 23, no. 5, 1031-1068, 2015. arXiv:1402.3457. Miroslav Bacak, B.H., Juergen Jost, Martin Kell and Armin Schikorra. A notion of nonpositive curvature for general metric spaces, Differential Geom. Appl., 38:22–32, arXiv:1404.0995, 2015. Jiao Gu, B.H. and Shiping Liu. Spectral distances on graphs, Discrete Appl. Math., 190/191, 56–74, 2015. arXiv:1402.6041. Ming Li, Tinggui Zhang, B.H., Shao-ming Fei and Xianqing Li-Jost, Quantum Nonlocality of Arbitrary Dimensional Bipartite States, Scientific Reports 5, 13358, 2015. B.H., Ming Li, Tinggui Zhang, Chunqin Zhou, Xianqing Li-Jost and Shao-Ming Fei, Towards Grothendieck constants and LHV models in quantum mechanics, J. Phys. A. 48, 065302, 2015. Tinggui Zhang, B.H., Ming Li, Mingjing Zhao and Hong Yang, A note on local unitary equivalence of isotropic-like states, Chin. Phys. B., 24, no. 12, 120305, 2015. Frank Bauer, B.H. and Juergen Jost. The dual Cheeger constant and spectra of infinite graphs, Adv. Math., 251: 147-194, 2014, arXiv:1207.3410. B.H. and Matthias Keller. Harmonic functions of general graph Laplacians, Calc. Var. Partial Differential Equations, 51 , no. 1-2, 343–362, arXiv:1303.7198, 2014. B.H. and Juergen Jost. Lq harmonic functions on graphs, Israel J. Math., 202, no.1, 475–490, arXiv:1301.3403, 2014. B.H. and Chao Xia. A note on local gradient estimate on Alexandrov spaces, Tohoku Math. J. (2), 66, no. 2, 259–267, arXiv:1301.4810, 2014. B.H., Shaoming Fei, Juergen Jost and Xianqing Li-Jost. The entanglement and separability of a special class of mixed states related to Hadamard matrices, Rep. Math. Phys., 74, no.1, 89–103, arXiv:1308.1505, 2014. Frank Bauer, B.H. and Matthias Keller. On the lp spectrum of Laplacians on graphs, Adv. Math., 248: 717-735, 2013,arXiv:1211.6536. B.H., Juergen Jost and Xianqing Li-Jost. Polynomial growth harmonic functions on finitely generated Abelian groups, Ann. Global Anal. Geom., 44 (4): 417-432, 2013, arXiv:1112.6284. B.H., Xiuhong Gao, Mingjing Zhao and Shaoming Fei. A note on resistance of NPT to mixture of separable states, Intern. J. Theor. Phys. 52 (9): 3007-3010, 2013. Frank Bauer, B.H., Jürgen Jost and Shiping Liu, Generalized Ricci curvature and the geometry of graphs, Actes des rencontres du CIRM 3 (2013), no. 1: Discrete curvature: Theory and applications, 69-78. B.H., Harmonic functions of polynomial growth on singular spaces with non-negative Ricci curvature, Proc. Amer. Math. Soc. 139 (6):2195-2205, 2011. B.H., Generalized Liouville theorem in nonnegatively curved Alexandrov spaces, Chin. Ann. Math. Ser. B 30 (2):111-128, 2009.

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