里奇曲率自下而上有界的可能坍缩空间的里奇曲率积分界值

IF 0.6 4区数学 Q3 MATHEMATICS

Differential Geometry and its Applications Pub Date : 2024-11-21 DOI:10.1016/j.difgeo.2024.102214

Michael Smith

引用次数: 0

摘要

假定完整黎曼流形的黎奇曲率有一个下限，对于 q<1/2，我们证明了黎奇曲率的局部 Lq norm 的边界存在，这些边界只取决于维数，并且随着体积塌缩而改善。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Integral Ricci curvature bounds for possibly collapsed spaces with Ricci curvature bounded from below

Assuming a lower bound on the Ricci curvature of a complete Riemannian manifold, for

q < 1 / 2

we show the existence of bounds on the local

L^{q}

norm of the Ricci curvature that depend only on the dimension and which improve with volume collapse.

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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.