中国科技论文在线

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2019年05月21日

【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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2019年05月20日

【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

摘要

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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2019年05月20日

【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

摘要

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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2019年05月20日

【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

摘要

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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2019年05月20日

【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

摘要

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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