Published papers:
Year 2023.
1. B.H. and Wendi Xu, Existence of ground state solutions to some nonlinear Schrödinger equations on lattice graphs. Calc. Var. Partial Differential Equations 62 (2023), no. 4, Paper No. 127, 17 pp.
2. 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.
3. 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.
4. 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.
5. Yohji Akama and B.H., Hyperbolic polyhedral surfaces with regular faces. Discrete Math. 346 (2023), no. 1, Paper No. 113213, 16 pp.
Year 2022.
1. 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.
2. B.H. and Yanhui Su, Total curvature of planar graphs with nonnegative combinatorial curvature. Trans. Amer. Math. Soc. 375 (2022), no. 12, 8423–8444.
3. 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.
4. B.H., Dimensional bounds for ancient caloric functions on graphs. Int. Math. Res. Not. IMRN 2022, no. 6, 4022–4039.
5. 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.
6. 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.
7. 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.
8. 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.
9. 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.
Year 2021.
1. Huabin Ge, B.H. and Zhou, Ze; Circle patterns on surfaces of finite topological type. Amer. J. Math. 143 (2021), no. 5, 1397–1430.
2. 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.
3. Huabin Ge, B.H. and Ze Zhou, Combinatorial Ricci flows for ideal circle patterns. Adv. Math. 383 (2021), Paper No. 107698, 26 pp.
4. B.H., Ancient caloric functions on graphs with unbounded Laplacians. Int. Math. Res. Not. IMRN 2021, no. 4, 3056–3077.
5. B.H. and Ruowei Li, The existence of extremal functions for discrete Sobolev inequalities on lattice graphs. J. Differential Equations 305 (2021), 224–241.
6. B.H., Jun Masamune, Radosław K. Wojciechowski, Essential self-adjointness and the L2-Liouville property. J. Fourier Anal. Appl. 27 (2021), no. 2, Paper No. 26, 27 pp.
7. 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.
8. 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.
9. B.H., Discrete harmonic functions on infinite penny graphs. Vietnam J. Math. 49 (2021), no. 2, 461–472.
Year 2020.
1. Huabin Ge and B.H., 3-dimensional combinatorial Yamabe flow in hyperbolic background geometry. Trans. Amer. Math. Soc. 373 (2020), no. 7, 5111–5140.
2. B.H. and Lili Wang, Dirichlet p-Laplacian eigenvalues and Cheeger constants on symmetric graphs. Adv. Math. 364 (2020), 106997, 34 pp.
3. 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.
4. Li Chen, Thierry Coulhon and B.H., Riesz transforms for bounded Laplacians on graphs. Math. Z. 294 (2020), no. 1-2, 397–417.
Year 2019.
1. 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.
2. B.H. and Florentin Münch, Radosław 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.
3. B.H. and Yong Lin, Graphs with large girth and nonnegative curvature dimension condition. Comm. Anal. Geom. 27 (2019), no. 3, 619–638.
4. 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.
Year 2018.
1. Huabin Ge and B.H., On combinatorial Calabi flow with hyperbolic circle patterns, Adv. Math., 333: 523–538, 2018.
2. B.H. and Luo Xin, Davies-Gaffney-Grigor’yan lemma on simplicial complexes, Math. Z. 290(2018), no. 3-4, 1041-1053.
3. Huabin Ge, B.H. and Wenfeng Jiang, A note on Liouville type equations on graphs, Proc. Amer. Math. Soc. 146 (2018), 4837–4842.
4. B.H. and Yan Huang, Neumann Cheeger constants on graphs. J. Geom. Anal. 28 (2018), no. 3, 2166–2184.
Year 2017.
1. Frank Bauer, B.H. and Shing-Tung Yau. Sharp Davies-Gaffney-Grigor’yan lemma on graphs, Math. Ann. 368(3-4): 1429–1437, 2017.
2. B.H. and Yong Lin, Stochastic completeness for graphs with curvature dimension conditions, Adv. Math., 306, 279–302, 2017.
3. 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.
4. 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.
Year 2016.
1. B.H. and Yong Lin, Curvature notions on graphs, Frontiers of Mathematics in China 11, no. 5, 1275–1290, 2016.
2. 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.
3. 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.
Year 2015
1. 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.
2. 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.
3. 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.
4. 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.
5. 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.
6. 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.
7. Jiao Gu, B.H. and Shiping Liu. Spectral distances on graphs, Discrete Appl. Math., 190/191, 56–74, 2015. arXiv:1402.6041.
8. 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.
9. 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.
10. 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.
Year 2014.
1. 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.
2. 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.
3. B.H. and Juergen Jost. Lq harmonic functions on graphs, Israel J. Math., 202, no.1, 475–490, arXiv:1301.3403, 2014.
4. 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.
5. 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.
Year 2013.
1. Frank Bauer, B.H. and Matthias Keller. On the lp spectrum of Laplacians on graphs, Adv. Math., 248: 717-735, 2013,arXiv:1211.6536.
2. 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.
3. 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.
4. 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.
Year 2011.
1. B.H., Harmonic functions of polynomial growth on singular spaces with non-negative Ricci curvature, Proc. Amer. Math. Soc. 139 (6):2195-2205, 2011.
Year 2009.
1. B.H., Generalized Liouville theorem in nonnegatively curved Alexandrov spaces, Chin. Ann. Math. Ser. B 30 (2):111-128, 2009.
Accepted papers:
2. Wen Han and Bobo Hua, Steklov eigenvalue problem on subgraphs of integer lattices, arXiv.1902.05831, to appear in Comm. Anal. Geom.
3. Bobo Hua and Zhiqin Lu, Graphs with positive spectrum, arXiv:2005.07985, to appear in J. London Math. Soc.
Preprints:
1. B.H., Martin Kell and Chao Xia. Harmonic functions on metric measure spaces, arXiv:1308.3607.
2. B.H. and Florentin Muench, Ricci curvature on birth-death processes, arXiv:1712.01494 .
3. Yohji Akama, B.H. and Yanhui Su, Areas of spherical polyhedral surfaces with regular faces, arXiv:1804.11033.
4. Yohji Akama, B.H., Yanhui Su, and Haohang Zhang, Graphs on surfaces with positive Forman curvature or corner curvature, arXiv: 2002.03550.
5. Fengwen Han and B.H., Uniqueness class of the wave equation on graphs, arXiv:2009.12793.
6. B.H. and Ariel Yadin, Universal inequalities for Dirichlet eigenvalues on discrete groups, arXiv:2007.13157.
7. Yohji Akama and B.H., Hyperbolic polyhedral surfaces with regular faces, arXiv:1807.10762.
8. Zunwu He and B.H., Steklov flflows on trees and applications, arXiv:2103.07696.
9. B.H. and Florentin M¨unch, Every Salami has two ends, arXiv:2105.11887.
