许洪伟
博士 教授 博士生导师
浙江大学 数学科学研究中心
整体微分几何、几何分析、流形拓扑学
个性化签名
- 姓名:许洪伟
- 目前身份:在职研究人员
- 担任导师情况:博士生导师
- 学位:博士
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学术头衔:
教育部“新世纪优秀人才支持计划”入选者, 博士生导师, 省学术和技术带头人等省级重要人才平台入选者
- 职称:高级-教授
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学科领域:
微分几何学
- 研究兴趣:整体微分几何、几何分析、流形拓扑学
许洪伟,男,1962年9月生。1990年在复旦大学获博士学位,师从胡和生院士。1990年任浙江大学讲师,当年成为浙江省第一位理科博士后;1993年任浙江大学副教授;1996年任浙江大学教授;2000年被评为博士生导师。历任几何与代数教研室主任、数学研究所党支部书记、数学系副主任、数学系常务副主任等职。2003年起,任浙江大学数学中心副主任。在《J. Differential Geom.》、《Geom. Funct. Anal.》、《Math. Ann.》、《J. Funct. Anal.》、《J. Math. Pures Appl.》、《Trans. Amer. Math. Soc.》等国内外重要刊物上发表论文70余篇。主持承担国家自然科学基金重点项目、面上项目等一系列国家级科研项目。获世界华人数学家联盟最佳论文奖、国家教育部科技成果奖各2项。任美国著名SCI数学期刊《Pure and Applied Math. Quarterly》执行主编。多次应邀在重要国际学术会议上作大会报告和特邀报告。入选国家教育部跨世纪优秀人才、浙江省151人才工程第一层次。
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主页访问
730
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关注数
1
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成果阅读
849
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成果数
10
【期刊论文】The topological sphere theorem for complete submanifolds
K. Shiohama, H. W. Xu
Compositio Math.,1997,107(2):221-232
1997年02月01日
A topological sphere theorem is obtained from the point of view of submanifold geometry. An important scalar is defined by the mean curvature and the squared norm of the second fundamental form of an oriented complete submanifold M in a space form of nonnegative sectional curvature. If the infimum of this scalar is negative, we then prove that the Ricci curvature of M has a positive lower bound. Making use of the Lawson-Simons formula for the nonexistence of stable k -currents, we eliminate the k-th homology group for all 1<k<n-1. We then observe that the fundamental group of M is trivial. It should be emphasized that our result is optimal.
the second fundamental form,, Ricci curvature,, integral homology,, stable currents
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114浏览
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2分享
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【期刊论文】On closed minimal submanifolds in pinched Riemannian manifolds
H. W. Xu
Trans. Amer. Math. Soc.,1995,347(2):1743-1751
1995年05月01日
In this paper, we prove the generalized Simons-Chern-do Carmo-Kobayashi-Lawson theorem for closed minimal submanifolds in pinched Riemannian manifolds.
closed minimal submanifolds, rigidity theorem, pinched Riemannian manifolds
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87浏览
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【期刊论文】The extension and convergence of mean curvature flow in higher comdimsion
K. F. Liu, H. W. Xu, F. Ye, E. T. Zhao
Trans. Amer. Math. Soc.,2018,370(3):2231-2262
2018年03月01日
In this paper, we investigate the convergence of the mean curvature flow of closed submanifolds in Euclidean space . We show that if the initial submanifold satisfies some suitable integral curvature conditions, then along the mean curvature flow it will shrink to a round point in finite time.
Mean curvature flow,, submanifold,, maximal existence time,, convergence theorem,, integral curvature
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78浏览
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【期刊论文】On Chern's conjecture for minimal hypersurfaces and rigidity of self-shrinkers
H. W. Xu, Z. Y. Xu, H. W. Xu, Z. Y. Xu
J. Funct. Anal.,2017,273(3):3406-3425
2017年09月26日
In this paper, we first give a refined version of Ding–Xin's rigidity theorem for minimal hypersurfaces in a sphere. We then improve Ding–Xin's rigidity theorem for self-shrinkers in the Euclidean space.
Chern conjecture for minimal hypersurfaces, Rigidity theorem, The second, fundamental form, Self-shrinker
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94浏览
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【期刊论文】A new characterization of the Clifford torus via scalar curvature pinching
H. W. Xu, Z. Y. Xu
J. Funct. Anal.,2014,267(3):3931-3962
2014年09月26日
We present a new characterization of the Clifford torus via scalar curvature pinching.
Hypersurfaces with constant mean curvature, Rigidity, Scalar curvature, Clifford torus
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79浏览
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【期刊论文】Geometric and differentiable rigidity of submanifolds in spheres
H. W. Xu, F. Huang, E. T. Zhao
J. Math. Pures Appl.,2013,99(1):330-342
2013年12月10日
In this paper, we investigate rigidity of geometric and differentiable structures of complete submanifolds via an extrinsic geometrical quantity τ(x) defined by the second fundamental form. We verify a geometric rigidity theorem for complete submanifolds with parallel mean curvature in a unit sphere. Inspired by the rigidity theorem, we prove a differentiable sphere theorem for complete submanifolds in a sphere . Moreover, we obtain a differentiable pinching theorem for complete submanifolds in a pinched Riemannian manifold.
Complete submanifolds, Geometric and differentiable structures, Rigidity, theorem, Ricci flow, Stable currents
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52浏览
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【期刊论文】The second pinching theorem for hypersurfaces with constant mean curvature in a sphere
H. W. Xu, Z. Y. Xu
Math. Ann.,2013,356(2):869-883
2013年08月20日
We prove the second pinching theorem for hypersurfaces with constant mean curvature in a sphere.
Hypersurfaces with constant mean curvature, the second pinching theorem, , the second fundamental form, Chern', s conjecture
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76浏览
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【期刊论文】Rigidity of Einstein manifolds with positive scalar curvature
H. W. Xu, J. R. Gu
Math. Ann.,2014,358(2):169-193
2014年06月20日
The purpose of this paper is to prove some new rigidity theorems for Einstein manifolds and submanifolds.
Einstein manifolds, rigidity theorems, positive scalar curvature
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96浏览
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【期刊论文】Geometric,topological and differentiable rigidity of submanifolds in space forms
H. W. Xu, J. R. Gu
Geom. Funct. Anal.,2013,23(1):1684-1703
2013年06月20日
In this paper, the authors investigate rigidity of geometric, topological and differentiable structures of compact submanifolds in a space form.
Submanifolds,, rigidity and sphere theorems,, Ricci curvature,, Ricci flow,, stable currents
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83浏览
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【期刊论文】The sphere theorem for manifolds with positive scalar curvature
J. R. Gu, H. W. Xu
Journal of Differential Geometry,2012,92(3):507-545
2012年05月17日
We prove some new differentiable sphere theorems via the Ricci flow and stable currents. We extend the sphere theorems in Riemannian geometry to submanifolds in a Riemannian manifold. We give a classification of submanifolds with weakly pinched curvatures, which improves the differentiable pinching theorems due to Andrews, Baker, and the authors. We also show that the Yau conjecture is false.
Differentiable sphere theorem, Ricci flow, stable currents, the Yau conjecture
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90浏览
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