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Minimal surfaces, surfaces of constant mean curvature and the mathematical theory of general relativity

Topic: Minimal surfaces, surfaces of constant mean curvature and the mathematical theory of general relativity
Talker: Prof. YE Rugang, University of California, Santa Barbara
Time: 2011-07-07 14:30--16:45
Address: 1208 room, Management & Research Building
Abstract:
1. First variation and second variation of area. Rectifiable currents. Existence and regularity of area-minimizing surfaces.
2. Basic consequences of stability. Nonnegative Ricci curvature and scalar curvature.
3. The Hawking mass. Complex structures. Conformal geometry. Divisors on Riemann surfaces.
4. Structures of stable minimal surfaces in 3-manifolds of positive scalar curvature.
5. Asymptotically flat manifolds. ADM mass. Schwarzschild space.
6. The positive mass theorem: the minimal surface approach of Schoen-Yau.
7. The positive mass theorem: the spinor approach of Witten.
8. Foliation by constant mean curvature spheres on asymptotically flat manifolds. Center of mass. Results of Huisken-Yau and Ye.
9. Geometric and topological structures of stable surfaces of constant mean curvature.
10.Strong uniqueness of stable spheres of constant mean curvature.