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Chen-Yun Lin

2012-06-21
14:00:00 - 15:00:00

308 , Mathematics Research Center Building (ori. New Math. Bldg.)

The problem of Weyl is a global isometric embedding problem. Consider the 2-sphere $(S^2,g_0)$ with positive Gauss curvature. Can the sphere be embedded into $(mathbb{R}^3,delta)$, where $delta$ is the standard flat metric. In this talk, I will discuss Nirenberg's proof using the continuity method. It involves three steps: (A) the space of $ds^2$ with positive curvature is connected, (B) the subset in the space which are realizable by convex surfaces is open which is attached by solving a system of linearized differential equations, and (C) closeness of the subset in (B).