论文标题
通过Riemannian Submanifolds急剧强烈的不平等现象
Sharp Hardy inequalities via Riemannian submanifolds
论文作者
论文摘要
本文专门针对riemannian环境中任意编码的子手法的距离功能的耐力不平等。在带有非负曲率的Riemannian歧管上，我们在submanifold既紧凑and not-compact and and compact的情况下都建立了几种尖锐的加权强壮不平等。特别是，即使环境歧管紧凑，这些不平等仍然有效，在这种情况下，我们找到了一个最佳的平滑功能空间来研究强壮的不平等现象。还提供了进一步的示例。我们的结果补充了最近在欧几里得和里曼尼亚环境中获得的几个方面。
This paper is devoted to Hardy inequalities concerning distance functions from submanifolds of arbitrary codimensions in the Riemannian setting. On a Riemannian manifold with non-negative curvature, we establish several sharp weighted Hardy inequalities in the cases when the submanifold is compact as well as non-compact. In particular, these inequalities remain valid even if the ambient manifold is compact, in which case we find an optimal space of smooth functions to study Hardy inequalities. Further examples are also provided. Our results complement in several aspects those obtained recently in the Euclidean and Riemannian settings.
