A Mean Curvature Type Flow in Space Forms
A Mean Curvature Type Flow in Space Forms
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DOI：
10.1093/imrn/rnu081
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发表时间：
2013-09
影响因子：
1
通讯作者：
Pengfei Guan;Junfang Li
中科院分区：
文献类型：
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作者：
Pengfei Guan;Junfang Li
本文在空间形式中引入了一类新的有界星形区域的平均曲率流，并在不作任何曲率假设的情况下证明了它的长期存在性和指数收敛性。沿着该流动，封闭体积是恒定的，并且表面积单调地演变。此外，对于Rn +1中的有界凸区域，证明了quermass积分沿着流单调发展，从而证明了quermass积分的一类Alexandrov-Fenchel不等式.
In this article, we introduce a new type of mean curvature flow for bounded star-shaped domains in space forms and prove its longtime existence, exponential convergence without any curvature assumption. Along this flow, the enclosed volume is a constant and the surface area evolves monotonically. Moreover, for a bounded convex domain in R n+1, the quermassintegrals evolve monotonically along the flow which allows us to prove a class of Alexandrov-Fenchel inequalities of quermassintegrals.