Profile
 
 

Hong-Wei Xu

Office: CMS 315, Zhejiang University 
Phone: (0571) 8795-3121
Fax: (0571) 8795-3035
E-mail:
xuhw@cms.zju.edu.cn

 

Education

  • B.A., East China Normal University, 1984.
  • M.A., East China Normal University, 1987.
  • Ph.D., Fudan University, 1990.

Experience

  • Professor, Zhejiang University, 1996—.
  • Visiting Professor, Kyushu University, 1994—1995.
  • Associate Professor, Zhejiang University, 1993—1996.
  • Lecturer, Zhejiang University, 1990—1993.

Teaching

  • Courses for Undergraduates: Differential Geometry, Differentiable Manifolds, Analytic Geometry, Higher Algebra, Seminar on Modern Mathematics I, II.
  • Courses for Graduates: Global Differential Geometry, Geometric Analysis, Curvature Flow in Geometry, Global Geometry of Submanifolds, Global Riemannian Geometry, Differentiable Manifolds and Geometry of Manifolds. 

Research Interest

  • Global Differential Geometry
  • Geometric Analysis
  • Topology of Manifolds
Selected Publications
.
[1] Y. X. Hu, H. W. Xu, and E. T. Zhao, First eigenvalue pinching for Euclidean hypersurfaces via k-th mean curvatures, Ann. Global Anal. Geom., 48(2015), 23-35.
[2] H. W. Xu and Z. Y. Xu, A new characterization of the Clifford torus via scalar curvature pinching, J. Funct. Anal., 267(2014), 3931-3962.
[3] H. W. Xu and J. R. Gu, Rigidity of Einstein manifolds with positive scalar curvature, Math. Ann., 358(2014), 169-193.
[4] C. Y. Xia and  H. W. Xu, Inequalities for eigenvalues of the drifting Laplacian on Riemannian manifolds, Ann. Global Anal. Geom., 45(2014), 155-166. 
[5] H. W. Xu, Y. Leng, and E. T. Zhao, Volume-preserving mean curvature flow of hypersurfaces in space forms,  Intern. J. Math., 25(2014), no. 3, 1450021, 19 pp.
[6] H. W. Xu, Y. Leng, and J. R. Gu, Geometric and Topological rigidity for compact submanifolds of odd dimension, Science China Math., 57(2014), 1525-1538.
[7] H. W. Xu and J. R. Gu, Geometric, topological and differentiable rigidity of submanifolds in space forms, Geom. Funct. Anal.,  23(2013), 1684-1703. 
[8] H. W. Xu and Z. Y. Xu, The second pinching theorem for hypersurfaces with constant mean curvature in a sphere, Math. Ann., 356(2013), 869-883.
[9] H. W. Xu, F. Huang, and E. T. Zhao, Geometric and differentiable rigidity of submanifolds in spheres, J. Math. Pures Appl., 99(2013), 330-342.
[10] K. F. Liu, H. W. Xu, F. Ye, and E. T. Zhao, Mean curvature flow of higher codimension in hyperbolic spaces, Comm. Anal. Geom., 21(2013), 651-669.
[11] J. R. Gu, H. W. Xu, Z. Y. Xu, and E. T. Zhao, A survey on rigidity problems in geometry and topology of submanifolds, Sixth International Congress of Chinese Mathematicians, AMS/IP, 2014.
[12] K. F. Liu, H. W. Xu, and E. T. Zhao, Some recent progress on mean curvature flow of arbitrary codimension, Sixth International Congress of Chinese Mathematicians, AMS/IP, 2014.
[13] J. R. Gu and H. W. Xu, The sphere theorem for manifolds with positive scalar curvature, Journal of Differential Geometry, 92(2012), 507-545.
[14] J. R. Gu and  H. W. Xu, On Yau rigidity theorem for minimal submanifolds in spheres, Math. Res. Lett., 19(2012), 511-523. 
[15] H. W. Xu, F. Huang, J. R. Gu and M. Y. He, L^{n/2} pinching theorem for submanifolds with parallel mean curvature in H^{n+p}(-1), Pure Appl. Math. Q., 8(2012), 1097-1116.
[16] H. W. Xu and F. Ye, Differentiable sphere theorems for submanifolds of positive k-th Ricci curvature, Manuscripta Math., 138(2012), 529-543.
[17] H. W. Xu and J. R. Gu, The differentiable sphere theorem for manifolds with positive Ricci curvature, Proc. Amer. Math. Soc., 140 (2012), 1011-1021
[18] H. W. Xu, Recent developments in differentiable sphere theorem, Fifth International Congress of Chinese Mathematicians, AMS/IP, Studies in Advanced Math., Vol.51, 2012,
pp.415-430.
[19] H. W. Xu and L. Tian, A differentiable sphere theorem inspired by rigidity of minimal submanifolds, Pacific J. Math., 254(2011), 499-510.
[20] K. Shiohama and H. W. Xu, An integral formula for Lipschitz-Killing curvature and the critical points of height functions, J. Geom. Analysis, 21(2011), 241–251.
[21] H. W. Xu, F. Ye and E. T. Zhao, Extend mean curvature flow with finite integral curvature, Asian J. Math., 15(2011), 549–556.
[22] H. W. Xu and L. Tian, A new pinching theorem for closed hypersurfaces with constant mean curvature in S^{n+1}, Asian J. Math., 15(2011), 611–630.
[23] H. W. Xu, F. Ye and E. T. Zhao, The extension for mean curvature flow with finite integral curvature in Riemannian manifolds, Science China Math., 54(2011), 2195–2204.
[24] H. W. Xu, F. Huang and F. Xiang, An extrinsic rigidity theorem for submanifolds with parallel mean curvature in a sphere, Kodai Math. J., 34(2011), 85–104.
[25] H. W. Xu and D. Y. Yang, The gap phenomenon for extremal submanifolds in a sphere, Differential Geom. and its Applications, 29(2011), 26–34.
[26] H. W. Xu and D. Y. Yang, A new characterization of Willmore submanifolds, Appl. Math. J. Chinese Univ., 26(2011), 453-463.
[27] H. W. Xu and J. R. Gu, An optimal differentiable sphere theorem for complete manifolds, Math. Res. Lett., 17(2010), 1111-1124.
[28] H. W. Xu and E. T. Zhao, L^p Ricci curvature pinching theorems for conformally flat Riemannian manifolds, Pacific J. Math., 245(2010), 381-396.
[29] H. P. Fu and H. W. Xu, Total curvature and L^2 harmonic 1-forms on complete submanifolds in space forms, Geom. Dedicata., 144(2010), 129-140.
[30] H. W. Xu and E. T. Zhao, Topological and differentiable sphere theorems for complete submanifolds, Comm. Anal. Geom., 17(2009), 565-585.
[31] H. W. Xu and E. T. Zhao, Complete hypersurfaces in a 4-dimensional hyperbolic space, Appl. Math. J. Chinese Univ., 24(2009), 370-378.
[32] H. P. Fu and H. W. Xu, Weakly stable constant mean curvature hypersurfaces, Appl. Math. J. Chinese Univ., 24(2009), 119-126.
[33] H. P. Fu and H. W. Xu, Vanishing and topological sphere theorems for submanifolds in a hyperbolic space, Intern. J. Math., 19(2008), 811-822. 
[34] H. W. Xu and X. Ren, Closed hypersurfurfaces with constant mean curvature in a symmetric manifold, Osaka J. Math., 45(2008), 747-756.
[35] H. W. Xu and J. F. Zhu, An optimal rigidity theorem for complete submanifolds in a sphere, Appl. Math. J. Chinese Univ., 23(2008), 219-226.
[36] H. W. Xu and J. R. Gu, A general gap theorem for submanifolds with parallel mean curvature in R^{n+p}, Comm. Anal. Geom., 15(2007)
175-193.
[37] S. M. Wei and H. W. Xu, Scalar curvature of minimal hypersurfaces in a sphere, Math. Res. Lett., 14(2007)
423-432.
[38] H. W. Xu and J. R. Gu, L^2-isolation phenomenon for complete surfaces arising from Yang-Mills theory, Lett. Math. Phys, 80(2007)
115-126.
[39] N. Q. Xie and H. W. Xu, Geometric inequalities for certain submanifolds in a pinched Riemannian manifold, Acta Math. Scientia, 27(2007)
611-618.
[40] Y. Leng and H. W. Xu, On complete submanifolds with parallel mean curvature in negative pinched manifolds, Appl. Math. J. Chinese Univ., 22(2007)
153-162.
[41] H. W. Xu and W. Zhang, Geometric properties for Gaussian image of submanifolds in $S^{n+p}$, Appl. Math. J. Chinese Univ., 22(2007)
371-377.
[42] H. W. Xu, Mean value theorem for critical points and sphere theorems, Proceedings of the Fourth ICCM, Vol.2, Higher Education Press & International Press, 2007,
pp.203-217.            
[43] H. W. Xu, W. Fang and F. Xiang, A generalization of Gauchman's rigidity theorem, Pacific J. Math., 228(2006)
185-199.
[44] L. Ji, J. S. Li, H. W. Xu and S. T. Yau, Lie Groups and Automorphic Forms, AMS/IP, Studies in Anvanced Math., Vol.37, 2006.
[45] H. W. Xu and W. Han, Geometric rigidity theorem for submanifolds with positive curvature, Appl. Math. J. Chinese Univ., 20(2005), 475-482.
[46] X. Ren and H. W. Xu, A lower bound for the first eigenvalue with mixed boundary condition, Appl. Math. J. Chinese Univ., 19(2004), 223-228.
 
[47] K. Shiohama and H. W. Xu, Rigidity and sphere theorems for submanifolds II, Kyushu J. Math., 54 (2000), 103-109.
[48] K. Shiohama and H. W. Xu, A general rigidity theorem for complete submanifolds, Nagoya Math. J., 150 (1998), 105-134.
[49] K. Shiohama and H. W. Xu, Lower bound for L^{n/2} curvature norm and its application, J. Geom. Analysis, 7(1997), 377-386.
[50] K. Shiohama and H. W. Xu, The topological sphere theorem for complete submanifolds, Compositio Math., 107 (1997), 221-232.
[51] H. W. Xu, On closed minimal submanifolds in pinched Riemannian manifolds, Trans. Amer.  Math. Soc., 347 (1995), 1743-1751. 
[52] H. W. Xu, L_{n/2} pinching theorems for submanifolds with parallel mean curvature in a sphere, J. Math. Soc. Japan, 46 (1994), 503-515.
[53] K. Shiohama and H. W. Xu, Rigidity and sphere theorems for submanifolds, Kyushu J. Math., 48 (1994), 291-306.
[54] H. W. Xu, Quantization phenomena for Riemannian submanifolds in Euclidean space, Interface between Phys. and Math., World Scientific, Singapore, 1994, pp.392-397.                   
[55] H. W. Xu, A rigidity theorem for submanifolds with parallel mean curvature in a sphere, Arch. der Math., 61 (1993), 489-496.
[56] H. W. Xu, Estimates of higher eigenvalues for minimal submanifolds, Differential Geometry, World Scientific, Singapore, 1993, pp.288-300.
[57] H. W. Xu, A pinching constant of Simons' type and the problem of isometric immersion. Chinese Ann. Math. Ser. A, 12(1991), 261–269.
 
.
Preprints
.
1.  Li Lei, Hongwei Xu: Mean curvature flow of arbitrary codimension in spheres and sharp differentiable sphere theorem,arXiv:1506.06371 [pdf, ps, other]
2.  Li Lei, Hongwei Xu: A New Version of Huisken's Convergence Theorem for Mean Curvature Flow in Spheres, arXiv:1505.07217 [pdf, ps, other]
3.  Li Lei, Hongwei Xu: An Optimal Convergence Theorem for Mean Curvature Flow of Arbitrary Codimension in Hyperbolic Spaces, arXiv:1503.06747 [pdf, ps, other]
4.  Kefeng Liu, Hongwei Xu, Entao Zhao: Mean curvature flow of higher codimension in Riemannian manifolds, arXiv:1204.0107 [pdf, ps, other]
5.  Kefeng Liu, Hongwei Xu, Entao Zhao: Deforming submanifolds of arbitrary codimension in a sphere, arXiv:1204.0106 [pdf, ps, other]
6.  Kefeng Liu, Hongwei Xu, Fei Ye, Entao Zhao: The extension and convergence of mean curvature flow in higher codimension, arXiv:1104.0971 [pdf, ps, other] 

 

 

 
Talks
 
Journals
  • Pure and Applied Mathematical Quarterly, Managing Editor.
  • Mathematics and Humanities, Editor.