Guoyi Xu

We study curvature pinching estimates of Ricci flow on complete threedimensional (3-dim) manifolds without bounded curvature assumption.We will derive some general curvature conditions which are preserved on any complete solution of 3-dim Ricci flow, these conditions include nonnegative Ricci curvature and sectional curvature as special cases.A local version of Hamilton-Ivey estimates is also obtained.

Ricci Flow

10.4310/mrl.2013.v20.n5.a3

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Citations (9)

The Rigidity and Stability of Gradient Estimates

Journal of Geometric Analysis (2022)

Qixuan Hu Guoyi Xu Chengjie Yu

Rigidity (electromagnetism)

Gaussian curvature

10.1007/s12220-022-01022-x

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Citations (1)

The sharp diameter bound of stable minimal surfaces

arXiv (Cornell University) (2024)

Qin Hu Guoyi Xu Shuai Zhang

For three dimensional complete Riemannian manifolds with scalar curvature no less than one, we obtain the sharp upper bound of complete stable minimal surfaces' diameter.

Minimal surface

10.48550/arxiv.2411.18928

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The first Dirichlet eigenvalue and the width

Journal of Functional Analysis (2024)

Guoyi Xu

Dirichlet eigenvalue

10.1016/j.jfa.2024.110709

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Short-time existence of the Ricci flow on noncompact Riemannian manifolds

Transactions of the American Mathematical Society (2013)

Guoyi Xu

In this paper, we give the first detailed proof of the short-time existence of Deane Yang’s local Ricci flow. Then, using the local Ricci flow, we prove the short-time existence of the Ricci flow on noncompact manifolds, whose Ricci curvature has global lower bound and sectional curvature has only local average integral bound. The short-time existence of the Ricci flow on noncompact manifolds with bounded curvature was studied by Wan-Xiong Shi in the 1990s. As a corollary of our main theorem, we obtain the short-time existence part of Shi’s theorem in this more general context.

Ricci Flow

Corollary

10.1090/s0002-9947-2013-05998-3

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Citations (18)

CCDC 726905: Experimental Crystal Structure Determination

The Cambridge Structural Database (2010)

Hongping Zhou Jian-Hui Yin Lingxia Zheng Peng Wang Fu‐Ying Hao

An entry from the Cambridge Structural Database, the world’s repository for small molecule crystal structures. The entry contains experimental data from a crystal diffraction study. The deposited dataset for this entry is freely available from the CCDC and typically includes 3D coordinates, cell parameters, space group, experimental conditions and quality measures.

10.5517/ccsddk3

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CCDC 721582: Experimental Crystal Structure Determination

The Cambridge Structural Database (2010)

Hongping Zhou Jian-Hui Yin Lingxia Zheng Peng Wang Fu‐Ying Hao

An entry from the Cambridge Structural Database, the world’s repository for small molecule crystal structures. The entry contains experimental data from a crystal diffraction study. The deposited dataset for this entry is freely available from the CCDC and typically includes 3D coordinates, cell parameters, space group, experimental conditions and quality measures.

10.5517/ccs6vvn

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The sharp lower bound of the first Dirichlet eigenvalue for geodesic balls

Mathematische Zeitschrift (2021)

Haibin Wang Guoyi Xu Jie Zhou

Ball (mathematics)

Dirichlet eigenvalue

Totally geodesic

Geodesic map

10.1007/s00209-021-02859-8

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Citations (1)

CCDC 675027: Experimental Crystal Structure Determination

The Cambridge Structural Database (2010)

Hongping Zhou Peng Wang Lingxia Zheng Wen-Qian Geng Jian-Hui Yin

An entry from the Cambridge Structural Database, the world’s repository for small molecule crystal structures. The entry contains experimental data from a crystal diffraction study. The deposited dataset for this entry is freely available from the CCDC and typically includes 3D coordinates, cell parameters, space group, experimental conditions and quality measures.

10.5517/ccqnf2v

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The construction of $$\epsilon $$-splitting map

Calculus of Variations and Partial Differential Equations (2023)

Guoyi Xu Jie Zhou

Ball (mathematics)

10.1007/s00526-022-02418-x

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Citations (1)