Curso - 24 aulas.

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.