非负曲率流形中子流形的直径估计

IF 0.6 4区数学 Q3 MATHEMATICS

Differential Geometry and its Applications Pub Date : 2023-10-01 DOI:10.1016/j.difgeo.2023.102048

Jia-Yong Wu

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引用次数: 0

摘要

给定一个光滑地浸入具有非负截面曲率的完全非紧黎曼流形中的闭连通流形，我们根据其平均曲率场积分来估计子流形的内直径。另一方面，对于边界光滑地浸入具有非负截面曲率的完全非紧黎曼流形中的紧致凸曲面，我们可以根据其平均曲率场积分和边界长度来估计其内直径。这些结果是对托平、吴征、彭前人工作的补充。

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Diameter estimates for submanifolds in manifolds with nonnegative curvature

Given a closed connected manifold smoothly immersed in a complete noncompact Riemannian manifold with nonnegative sectional curvature, we estimate the intrinsic diameter of the submanifold in terms of its mean curvature field integral. On the other hand, for a compact convex surface with boundary smoothly immersed in a complete noncompact Riemannian manifold with nonnegative sectional curvature, we can estimate its intrinsic diameter in terms of its mean curvature field integral and the length of its boundary. These results are supplements of previous work of Topping, Wu-Zheng and Paeng.

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来源期刊

Differential Geometry and its Applications 数学-数学

CiteScore

1.00

自引率

20.00%

发文量

审稿时长

6-12 weeks

期刊介绍： Differential Geometry and its Applications publishes original research papers and survey papers in differential geometry and in all interdisciplinary areas in mathematics which use differential geometric methods and investigate geometrical structures. The following main areas are covered: differential equations on manifolds, global analysis, Lie groups, local and global differential geometry, the calculus of variations on manifolds, topology of manifolds, and mathematical physics.