Speaker：Dr. Changwei Xiong

                        The Australian National University

Title:  Convexity of nonnegatively curved hypersurfaces with free boundary on a sphere

       Time：28 May 2019,15:00

Location：实验楼108

Abstract:  When is an immersed hypersurface in Euclidean space globally convex? One answer obtained by Hadamard in 1897 is that, any closed immersed surface with positive Gaussian curvature in 3-dimensional Euclidean space must be the boundary of a convex body. After the later efforts by Stoker, van Heijenoort, Chern--Lashof, and Sacksteder, the answer for hypersurfaces without boundary now is quite complete. In this talk we shall focus on this problem for hypersurfaces with boundary. More precisely, our work shows that any compact immersed hypersurface in Euclidean space with nonnegative sectional curvatures and with free boundary on the standard sphere must be globally convex. The key ingredient in the proof is a gluing process which reduces the problem with boundary to that without boundary. This work is joint with Mohammad Ghomi.

   Speaker Introduction：熊昌伟，2015年博士毕业于清华大学，从2015年起在澳大利亚国立大学从事博士后研究工作，主要从事几何流、自由边值曲面等几何分析问题，在Adv. Math.,  Calc.Var., JGA, JFA等数学一流期刊上发表论文十余篇。

 联系人：  夏超教授