Programa de Doutorado 2011: Minimal Surfaces

The Theory of Minimal Submanifolds: The equations of minimal submanifolds and examples. The first and second variation formulas of volume, and stability. Bernsteins' theorem, the Weierstrass representation and the strong maximum principle. Multi-valued minimal graphs.
Curvature Estimates: Simons, inequality. Small energy curvature estimates for minimal surfaces. L^p curvature bounds for stable hypersurfaces. Almost stability. Minimal cones.
Existence of Minimal Surfaces: The Plateau problem and its solution. Harmonic maps. Existence of minimal spheres in a homotopy class.
Minimal Surfaces in Three-Manifolds: Hersch's and Yang-Yau's Theorem. The Reilly Formula. Choi and Wang's estimate. Compactness Theorems with a priori bounds. The positive mass theorem.
Colding-Minicozzi Theory: The structure of embedded minimal disks. Compactness Theorems without a priori bounds.

 

Vídeos

Minimal Surfaces

Harold Rosenberg

Aula 01 - 15.03.2011 - download
Aula 02 - 17.03.2011 - download
Aula 03 - 22.03.2011 - download
Aula 04 - 24.03.2011 - download
Aula 05 - 29.03.2011 - download
Aula 06 - 31.03.2011 - download
Aula 07 - 13.04.2011 - download
Aula 08 - 14.04.2011 - download *
Aula 09 - 19.04.2011 - download
Aula 10 - 26.04.2011 - download
Aula 11 - 28.04.2011 - download
Aula 12 - 03.05.2011 - download
Aula 13 - 05.05.2011 - download
Aula 14 - 10.05.2011 - download
Aula 15 - 12.05.2011 - download
Aula 16 - 17.05.2011 - download
Aula 17 - 19.05.2011 - download
Aula 18 - 24.05.2011 - download
Aula 19 - 26.05.2011 - download
Aula 20 - 31.05.2011 - download
Aula 21 - 02.06.2011 - download
Aula 22 - 07.06.2011 - download
Aula 23 - 09.06.2011 - download
Aula 24 - 14.06.2011 - download - FINAL
* Devido a um problema técnico, o vídeo da aula está incompleto.

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