中文 Tsinghua University Access to the old version Talent Recruitment

Li Haizhong

  • Professor
  • Tel:
  • Email: lihz@tsinghua.edu.cn

Education

PhD 1992, University of Novi Sad (former Yugoslavia)

Work Experience

1993.09-1995.07, postdoctor, the Chinese Academy of Sciences

1995.07-1998.07, associate professor, Department of Mathematical Sciences, Tsinghua University

1998.08-Now, professor, Department of Mathematical Sciences, Tsinghua University

1999.09-2000.07, visit scholar, Department of Mathematics, Harvard University

2001.07-2002.12, Alexander von Humboldt Fellow, TU Berlin

Research Interests

1. Differential Geometry

2. Geometric Analysis.

Teaching

1. Differential Geometry

2. Riemannian Geometry

3. Differentiable Manifold

4. Geometry of hypersurfaces and curvature flows

5. Topics on Geometry

Selected Publications

[LW25] Li, Haizhong; Wan, Yao; Classification of solutions to the isotropic horospherical p-Minkowski problem in hyperbolic plane. J. Math. Phys. 66 (2025), no. 8, Paper No. 081515, 16 pp.

[GLW25] Gu, Pingxin; Li, Haizhong; Wan, Yao; Weinstock inequality in hyperbolic space. J. Funct. Anal. 289 (2025), no. 12, Paper No. 111155, 22 pp.

[GLX25]Guo, Jinyu; Li, Haizhong; Xia, Chao; Stable (r+1)-th capillary hypersurfaces. Rev. Mat. Iberoam. 41 (2025), no. 5, 1629–1664.

[LLX25] Li, Haizhong; Li, Ruixuan; Xiong, Changwei; Sharp upper bounds for the capacity in the hyperbolic and Euclidean spaces. Adv. Nonlinear Anal. 14 (2025), no. 1, Paper No. 20250068, 21 pp.

[GL25] Gu, Pingxin; Li, Haizhong; A proof of Guo-Wang's conjecture on the uniqueness of positive harmonic functions in the unit ball. Math. Ann. 391 (2025), no. 3, 3501-3517.

[HLZ25] Hong, Han; Li, Haizhong; Zhang, Meng; Asymptotic plateau problem via equidistant hyperplanes. J. Geom. Anal. 35 (2025), no. 2, Paper No. 53, 34 pp.

[LWX24]Li, Haizhong; Wan, Yao; Xu, Botong; The discrete horospherical p-Minkowski problem in hyperbolic space. Adv. Math. 453 (2024), Paper No. 109851, 31 pp.

[LLWY24] Li, Haizhong; Vrancken, Luc; Wang, Xianfeng; Yao, Zeke; Hypersurfaces of S2×S2 with constant sectional curvature. Calc. Var. Partial Differential Equations 63 (2024), no. 7, Paper No. 167, 33 pp.

[LZ24] Li, Haizhong; Zhang, Ruijia A flow approach to the prescribed Gaussian curvature problem in Hn+1. Adv. Calc. Var. 17 (2024), no. 3, 521–543.

[LW24] Li, Haizhong; Wan, Yao; Uniqueness of solutions to some classes of anisotropic and isotropic curvature problems. J. Funct. Anal. 287 (2024), no. 3, Paper No. 110471, 30 pp.

[CLW223] Chen, Daguang; Li, Haizhong; Wei, Yilun; Comparison results for solutions of Poisson equations with Robin boundary on complete Riemannian manifolds. Internat. J. Math. 34 (2023), no. 8, Paper No. 2350045, 19 pp.

[LW23]Li, Haizhong; Wan, Yao; The Christoffel problem in the hyperbolic plane. Adv. in Appl. Math. 150 (2023), Paper No. 102557, 17 pp.

[LX23] Li, Haizhong; Xu, Botong; A class of weighted isoperimetric inequalities in hyperbolic space. Proc. Amer. Math. Soc. 151 (2023), no. 5, 2155–2168.

[CL23] Chen, Daguang; Li, Haizhong; Talenti's comparison theorem for Poisson equation and applications on Riemannian manifold with nonnegative Ricci curvature. J. Geom. Anal. 33 (2023), no. 4, Paper No. 123, 20 pp.

[HLi-23] Hu, Yingxiang; Li, Haizhong; Blaschke-Santaló type inequalities and quermassintegral inequalities in space forms. Adv. Math. 413 (2023), Paper No. 108826, 31 pp.

[CCL-22] Chen, Daguang; Cheng, Qing-Ming; Li, Haizhong; Faber-Krahn inequalities for the Robin Laplacian on bounded domain in Riemannian manifolds. J. Differential Equations 336 (2022), 374–386.

[HLi-22] Hu, Yingxiang; Li, Haizhong; Geometric inequalities for static convex domains in hyperbolic space. Trans. Amer. Math. Soc. 375 (2022), no. 8, 5587–5615.

[GLW-22] Gao, Shanze; Li, Haizhong; Wang, Xianfeng; Self-similar solutions to fully nonlinear curvature flows by high powers of curvature. J. Reine Angew. Math. 783 (2022), 135–157.

[HLW-22] Hu, Yingxiang; Li, Haizhong; Wei, Yong; Locally constrained curvature flows and geometric inequalities in hyperbolic space. Math. Ann. 382 (2022), no. 3-4, 1425–1474.

[LXZ-22] Li, Haizhong; Xu, Botong; Zhang, Ruijia; Asymptotic convergence for a

class of anisotropic curvature flows. J. Funct. Anal. 282 (2022), no. 12, Paper

No. 109460, 34 pp.

[LWW-21] Li, Haizhong; Wang, Xianfeng; Wu, Jing; Contracting axially

symmetric hypersurfaces by powers of the σ_k-curvature. J. Geom. Anal. 31

(2021), no. 3, 2656–2702.

[AHL-20] Andrews, Ben; Hu, Yingxiang; Li, Haizhong; Harmonic mean

curvature flow and geometric inequalities. Adv. Math. 375 (2020), 107393, 28 pp.

[HLW-20] Hu, Yingxiang; Li, Haizhong; Wei, Yong; Zhou, Tailong; Contraction of

surfaces in hyperbolic space and in sphere. Calc. Var. Partial Differential

Equations 59 (2020), no. 5, Paper No. 172, 32 pp.

[CLZ-19] Chen, Daguang; Li, Haizhong; Zhou, Tailong; A Penrose type inequality

for graphs over Reissner-Nordström–anti-deSitter manifold. J. Math.

Phys. 60 (2019), no. 4, 043503, 12 pp

[HLi-19] Hu, Yingxiang; Li, Haizhong; Geometric inequalities for hypersurfaces

with nonnegative sectional curvature in hyperbolic space. Calc. Var. Partial

Differential Equations 58 (2019), no. 2, Paper No. 55, 20 pp.

[LWW-19] Li, Haizhong; Wang, Xianfeng; Wei, Yong; Surfaces expanding by non-concave curvature functions. Ann. Global Anal. Geom. 55 (2019), no. 2, 243–279.

[CLW-18] Chen, Daguang; Li, Haizhong; Wang, Zhizhang; Starshaped compact

hypersurfaces with prescribed Weingarten curvature in warped product

manifolds. Calc. Var. Partial Differential Equations 57 (2018), no. 2, Paper No. 42,

26 pp.

[GLM-18] Gao, Shanze; Li, Haizhong; Ma, Hui; Uniqueness of closed self-similar solutions to σαk-curvature flow. NoDEA Nonlinear Differential Equations Appl. 25 (2018), no. 5, Paper No. 45, 26 pp.

[LiX-18] Li, Haizhong; Xiong, Changwei; Stability of capillary hypersurfaces in a Euclidean ball. Pacific J. Math. 297 (2018), no. 1, 131–146.

[LW1-17] Li, Haizhong; Wang, Xianfeng; New characterizations of the Clifford torus as a Lagrangian self-shrinker. J. Geom. Anal. 27 (2017), no. 2, 1393–1412.

[LW2-17] Li, Haizhong; Wei, Yong; On inverse mean curvature flow in Schwarzschild space and Kottler space. Calc. Var. Partial Differential Equations 56 (2017), no. 3, Paper No. 62, 21 pp.

[ALi-15] Andrews, Ben; Li, Haizhong; Embedded constant mean curvature tori in the three-sphere. J. Differential Geom. 99 (2015), no. 2, 169--189.

[AHL-15] Andrews, Ben; Han, Xiaoli; Li, Haizhong; Wei, Yong; Non-collapsing for hypersurface flows in the sphere and hyperbolic space. Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 14 (2015), no. 1, 331–338.

[LW1-15] Li, Haizhong; Wei, Yong; f-minimal surface and manifold with positive m-Bakry-Émery Ricci curvature. J. Geom. Anal. 25 (2015), no. 1, 421–435.

[LW2-15] Li, Haizhong; Wei, Yong; Rigidity theorems for diameter estimates of compact manifold with boundary. Int. Math. Res. Not. IMRN 2015, no. 11, 3651–3668.

[ALW-14] Andrews, Ben; Li, Haizhong; Wei, Yong; F-stability for self-shrinking solutions to mean curvature flow. Asian J. Math. 18 (2014), no. 5, 757–777.

[LiW-14] Li, Haizhong; Wang, Xianfeng; A differentiable sphere theorem for compact Lagrangian submanifolds in complex Euclidean space and complex projective space. Comm. Anal. Geom. 22 (2014), no. 2, 269–288.

[LWX-14] Li, Haizhong; Wei, Yong; Xiong, Changwei; A geometric inequality on hypersurface in hyperbolic space. Adv. Math. 253 (2014), 152–162.

[LW1-4] Li, Haizhong; Wei, Yong; Classification and rigidity of self-shrinkers in the mean curvature flow. J. Math. Soc. Japan 66 (2014), no. 3, 709–734.

[CLi-13] Cao, Huai-Dong; Li, Haizhong; A gap theorem for self-shrinkers of the mean curvature flow in arbitrary codimension. Calc. Var. Partial Differential Equations 46 (2013), no. 3-4, 879–889.

[FLL-13] Futaki, Akito; Li, Haizhong; Li, Xiang-Dong; On the first eigenvalue of the Witten-Laplacian and the diameter of compact shrinking solitons. Ann. Global Anal. Geom. 44 (2013), no. 2, 105–114.

[HHL-13] Huang, Guangyue; Huang, Zhijie; Li, Haizhong Gradient estimates for the porous medium equations on Riemannian manifolds. J. Geom. Anal. 23 (2013), no. 4, 1851–1875.

[DLV-12] Dillen, Franki; Li, Haizhong; Vrancken, Luc; Wang, Xianfeng; Lagrangian submanifolds in complex projective space with parallel second fundamental form. Pacific J. Math. 255 (2012), no. 1, 79–115.

[LMW-12] Li, Haizhong; Ma, Hui; Wei, Guoxin; A class of minimal Lagrangian submanifolds in complex hyperquadrics. Geom. Dedicata 158 (2012), 137–148.

[CLi-11] Chen, Daguang; Li, Haizhong; Second eigenvalue of Paneitz operators and mean curvature. Comm. Math. Phys. 305 (2011), no. 3, 555–562.

[GLi-11] Guo, Bin; Li, Haizhong; The second variational formula for the functional ∫v(6)(g)dVg. Proc. Amer. Math. Soc. 139 (2011), no. 8, 2911–2925.

[GHL-11] Guo, Bin; Han, Zheng-Chao; Li, Haizhong; Two Kazdan-Warner-type identities for the renormalized volume coefficients and the Gauss-Bonnet curvatures of a Riemannian metric. Pacific J. Math. 251 (2011), no. 2, 257–268.

[HLV-11] Hu, Zejun; Li, Haizhong; Vrancken, Luc; Locally strongly convex affine hypersurfaces with parallel cubic form. J. Differential Geom. 87 (2011), no. 2, 239--307.

[HLL-11] Hu, Zejun; Li, Cece; Li, Haizhong; Vrancken, Luc; Lorentzian affine hypersurfaces with parallel cubic form. Results Math. 59 (2011), no. 3-4, 577–620.

[HLM-09] He, Yijun; Li, Haizhong; Ma, Hui; Ge, Jianquan; Compact embedded hypersurfaces with constant higher order anisotropic mean curvatures. Indiana Univ. Math. J. 58 (2009), no. 2, 853–868.

[HL1-08] He, Yijun; Li, Haizhong; Integral formula of Minkowski type and new characterization of the Wulff shape. Acta Math. Sin. (Engl. Ser.) 24 (2008), no. 4, 697–704.

[HL2-08] He, Yijun; Li, Haizhong; Stability of hypersurfaces with constant (r+1)-th anisotropic mean curvature. Illinois J. Math. 52 (2008), no. 4, 1301–1314.

[LMS-08] Li, Haizhong; Ma, Hui; Su, Linlin; Lagrangian spheres in the 2-dimensional complex space forms. Israel J. Math. 166 (2008), 113–124.

[CLi-07] Cao, Linfen; Li, Haizhong; r-minimal submanifolds in space forms. Ann. Global Anal. Geom. 32(2007), no. 4, 311–341.

[CLU-06] Castro, Ildefonso; Li, Haizhong; Urbano, Francisco; Hamiltonian-minimal Lagrangian submanifolds in complex space forms. Pacific J. Math. 227 (2006), no. 1, 43–63.

[LiV-05] Li, Haizhong; Vrancken, Luc; A basic inequality and new characterization of Whitney spheres in a complex space form. Israel J. Math. 146 (2005), 223–242.

[HL1-04] Hu, Zejun; Li, Haizhong; A new variational characterization of n-dimensional space forms. Trans. Amer. Math. Soc. 356 (2004), no. 8, 3005–3023.

[HL2-04] Hu, Zejun; Li, Haizhong; Classification of hypersurfaces with parallel Möbius second fundamental form in Sn+1. Sci. China Ser. A 47 (2004), no. 3, 417–430.

[Lih-04] Li, Haizhong; A sextic holomorphic form of affine surfaces with constant affine mean curvature. Arch. Math. (Basel) 82 (2004), no. 3, 263–272.

[HLi-03] Hu, Zejun; Li, Haizhong; Submanifolds with constant Möbius scalar curvature in Sn. Manuscripta Math. 111 (2003), no. 3, 287–302.

[LiS-03] Li, Haizhong; Simon, Udo; Quantization of curvature for compact surfaces in Sn. Math. Z. 245(2003), no. 2, 201–216.

[LiW-03] Li, Haizhong; Wang, Changping; Möbius geometry of hypersurfaces with constant mean curvature and scalar curvature. Manuscripta Math. 112 (2003), no. 1, 1–13.

[LiV-03] Li, Haizhong; Vrancken, Luc; New examples of Willmore surfaces in Sn. Ann. Global Anal. Geom. 23(2003), no. 3, 205–225.

[Lih-02] Li, Haizhong; Willmore submanifolds in a sphere. Math. Res. Lett. 9 (2002), no. 5-6, 771–790.

[LLW-02] Li, Haizhong; Liu, Huili; Wang, Changping; Zhao, Guosong; Möbius isoparametric hypersurfaces in Sn+1 with two distinct principal curvatures. Acta Math. Sin. (Engl. Ser.) 18 (2002), no. 3, 437–446.

[GLW-01] Guo, Zhen; Li, Haizhong; Wang, Changping; The second variational formula for Willmore submanifolds in Sn. Dedicated to Shiing-Shen Chern on his 90th birthday. Results Math. 40 (2001), no. 1-4, 205–225.

[Lih-01] Li, Haizhong; Willmore hypersurfaces in a sphere. Asian J. Math. 5 (2001), no. 2, 365–377.

[LW1-01] Haizhong; Wang, Changping; Wu, Faen; A Moebius characterization of Veronese surfaces in Sn. Math. Ann. 319 (2001), no. 4, 707–714.

[LW2-02] Li, Haizhong; Wang, Changping; Wu, Faen; The classification of homogeneous 2-spheres in CPn. Asian J. Math. 5 (2001), no. 1, 93–108.

[CLi-97] Chen, Weihuan; Li, Haizhong; Bonnet surfaces and isothermic surfaces. Results Math. 31 (1997), no. 1-2, 40–52.

[Li1-97] Li, Haizhong; Global rigidity theorems of hypersurfaces. Ark. Mat. 35 (1997), no. 2, 327–351.

[Li2-97] Li, Haizhong; Complete spacelike submanifolds in de Sitter space with parallel mean curvature vector satisfying H2=4(n−1)/n2. Ann. Global Anal. Geom. 15 (1997), no. 4, 335–345.

[Li3-97] Li, Haizhong; Generalized Cartan identities on isoparametric manifolds. Ann. Global Anal. Geom. 15(1997), no. 1, 45–50.

[Lih-96] Li, Haizhong; Hypersurfaces with constant scalar curvature in space forms. Math. Ann. 305 (1996), no. 4, 665–672.