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

IF 0.6 4区 数学 Q3 MATHEMATICS
Michael Smith
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引用次数: 0

Abstract

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 Lq norm of the Ricci curvature that depend only on the dimension and which improve with volume collapse.
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
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。
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来源期刊
CiteScore
1.00
自引率
20.00%
发文量
81
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.
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