论文标题
Minkowski的不平等和弯曲空间中的逆弯曲流动限制
Minkowski inequalities and constrained inverse curvature flows in warped spaces
论文作者
论文摘要
本文涉及在一系列Riemannian扭曲的空间中局部受约束的逆弯曲流。对于某些类别的流量，我们证明了很长的存在和平滑的收敛到径向坐标切片。在二维表面和合适的速度的情况下，这些流量具有两个单调量。在这种情况下，新的Minkowski类型不平等是结果。在较高的维度中，当环境径向RICCI曲率持续负面时，我们使用反平均曲率流以获得新的Minkowski不平等。
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.
