报告名称：A new phenomenon involving inverse curvature flows in hyperbolic space

主办单位：数学科学学院

报告专家：王险峰

专家所在单位：南开大学

报告时间：2020年9月30日10：00-12：00

报告地点：腾讯会议（会议ID：978 144 246）

专家简介：王险峰，南开大学副教授。

报告摘要：Inverse curvature flows for hypersurfaces in hyperbolic space have been investigated intensively in recent years. In 2015, Hang and Wang constructed an example to show that the limiting shape of the inverse mean curvature flow in hyperbolic space is not necessarily round after scaling. This was extended by Li, Wang and Wei in 2016 to the inverse curvature flow in hyperbolic space by $H^{-p}$ with power $p\in(0,1)$. Recently, we discover a new phenomenon involving inverse curvature flows in hyperbolic space. We find that for a large class of symmetric and 1-homogeneous curvature functions $F$ of the shifted Weingarten matrix $\mathcal{W}-I$, the inverse curvature flow with initial horospherically convex hypersurface in hyperbolic space and driven by $F^{-p}$ with $p\in(0,1]$ will expand to infinity in finite time. The flow is asymptotically round smoothly and exponentially as the maximum time is approached, which means that the flow becomes exponentially close to a flow of geodesic spheres. We also construct a counterexample to show that our results cannot be extended to the case with power $p>1$. This is a joint work with Prof. Yong Wei and Dr. Tailong Zhou.

邀请人：涂强