Insufficient convergence of inverse mean curvature flow on asymptotically hyperbolic manifolds
Insufficient convergence of inverse mean curvature flow on asymptotically hyperbolic manifolds
复制标题
DOI：
10.4310/jdg/1271271798
复制
发表时间：
2007-11
影响因子：
2.5
通讯作者：
A. Neves
中科院分区：
文献类型：
--
作者：
A. Neves
我们构造了一个渐近双曲三维流形上的反平均曲率流的解，它不具有证明Penrose型不等式所需的收敛性质。这与渐近平坦的情况形成鲜明对比。其主要思想是在结合反平均曲率流所做的工作，石潭关于紧流形的边界行为。假设Penrose不等式成立，我们还得到了S上函数的一个非平凡不等式。
We construct a solution to inverse mean curvature flow on an asymptotically hyperbolic 3-manifold which does not have the convergence properties needed in order to prove a Penrose–type inequality. This contrasts sharply with the asymptotically flat case. The main idea consists in combining inverse mean curvature flow with work done by Shi–Tam regarding boundary behavior of compact manifolds. Assuming the Penrose inequality holds, we also derive a nontrivial inequality for functions on S.