报告人：韦勇博士

             澳大利亚国立大学

题目：Volume preserving flow and Alexandrov-Fenchel inequalities in hyperbolic space

时间：2018年07月17日下午14:30

地点：海韵数理楼661

摘要：I will describe my recent work with Ben Andrews and Xuzhong Chen on volume preserving flow and Alexandrov-Fenchel inequalities in hyperbolic space. First, if the initial hypersurface in hyperbolic space has positive sectional curvature, we show that a large class of volume preserving flow preserves the positivity of sectional curvatures, and the flow converges smoothly to a geodesic sphere. This result can be used to show that certain Alexandrov-Fenchel quermassintegral inequalities, known previously for horospherical convex hypersurfaces (by G.Wang and C.Xia (2013)), also hold under the weaker condition of positive sectional curvature. Second, we consider the volume preserving flow of strictly horospherically convex hypersurfaces in hyperbolic space by function of shifted principal curvatures, and apply the convergence result to prove a new class of Alexandrov-Fenchel type inequalities for horospherically convex hypersurfaces.

报告人简介：韦勇于2014年在清华大学获得博士学位，2014-2016年在英国伦敦college大学从事博士后，目前是 澳大利亚国立大学的高级博士后。他的研究方向是微分几何与几何分析，目前的兴趣包括超曲面几何流, G2几何中的Laplace流等。他在Geom. Funct. Anal., J. Differ. Geom., Adv. Math.等一流数学杂志上发表论文20余篇。

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