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Convexity of nonnegatively curved hypersurfaces with free boundary on a sphere

来源:复旦大学数学科学学院 | 2019-03-13 | 发布:经管之家

报告题目: Convexity of nonnegatively curved hypersurfaces with free boundary on a sphere报 告 人:熊昌伟报告人所在单位:澳大利亚国立大学报告日期:2019-04-02 星期二报告时间:10:00--11:00报告地点:光华楼东主楼2001报告摘要:
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.

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