Minkowski inequalities and constrained inverse curvature flows in warped spaces
Minkowski inequalities and constrained inverse curvature flows in warped spaces
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DOI：
10.1515/acv-2020-0050
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发表时间：
2020-05
影响因子：
1.7
通讯作者：
Julian Scheuer
中科院分区：
文献类型：
--
作者：
Julian Scheuer
摘要本文研究了一类广义黎曼翘曲空间中的局部约束反曲率流。对于一类这样的流，我们证明了长时间的存在性和光滑收敛到一个径向坐标切片。在二维表面和适当的速度的情况下，这些流享有两个单调量。在这种情况下，新的Minkowski型不等式的后果。在高维情形下，当环境径向Ricci曲率为常负时，我们利用反平均曲率流得到了新的Minkowski不等式。
Abstract This paper deals with locally constrained inverse curvature flows in a broad class of Riemannian warped spaces. For a certain class of such flows, we prove long-time existence and smooth convergence to a radial coordinate slice. In the case of two-dimensional surfaces and a suitable speed, these flows enjoy two monotone quantities. In such cases, new Minkowski type inequalities are the consequence. In higher dimensions, we use the inverse mean curvature flow to obtain new Minkowski inequalities when the ambient radial Ricci curvature is constantly negative.