论文标题
在双曲线空间中移动的逆弯曲流动
Shifted inverse curvature flows in hyperbolic space
论文作者
论文摘要
我们介绍了双曲线空间中移动的反向曲率流。这是双曲线空间中的一系列Hypersurfaces家族，$ f^{ - p} $，正功率$ p $，用于平滑，对称，严格增加和$ 1 $的均匀曲率函数$ f $ f $ f $ f $ f $ f $ f $ f $ f $ f $ f $ f $ f $ f $ f $ f $ f $ f $ f $ f $ f $。我们研究Horo-Convex Hypersurfaces流动的最大存在和渐近行为。特别是，对于$ 0 <p \ leq 1 $，我们显示解决方案的限制形状始终是圆形的，因为接近最大的存在时间。这与悬挂和王[18]构造了反例，以表明双曲线空间中逆向曲率流的极限形状不一定是圆形的，这与（不移位）反向曲率流的渐近行为形成鲜明对比。
We introduce the shifted inverse curvature flow in hyperbolic space. This is a family of hypersurfaces in hyperbolic space expanding by $F^{-p}$ with positive power $p$ for a smooth, symmetric, strictly increasing and $1$-homogeneous curvature function $f$ of the shifted principal curvatures with some concavity properties. We study the maximal existence and asymptotical behavior of the flow for horo-convex hypersurfaces. In particular, for $0<p\leq 1$ we show that the limiting shape of the solution is always round as the maximal existence time is approached. This is in contrast to the asymptotical behavior of the (non-shifted) inverse curvature flow, as Hung and Wang [18] constructed a counterexample to show that the limiting shape of inverse curvature flow in hyperbolic space is not necessarily round.
