Geometric analysis : partial differential equations and surfaces : UIMP-RSME Santaló Summer School 2010 : Geometric analysis, June 28-July 2, 2010, University of Granada, Spain / Joaquín Pérez, José A. Galvez, editors
Published
Providence, R.I. : American Mathematical Society, 2012
""Preface""; ""Geometric PDEs in the presence of isolated singularities""; ""1. Introduction""; ""2. The Hessian one equation: preliminaries""; ""3. Isolated singularities of â??â?? _{ }- _{ }²=1: local study""; ""4. Isolated singularities of â??â?? _{ }- _{ }²=1: global study""; ""5. Surfaces of constant curvature in â??³""; ""6. Isolated singularities of the constant curvature equation""; ""7. Immersed isolated singularities""; ""8. Peaked spheres in â??³""; ""9. Further results and open problems""; ""References""
""Constant mean curvature surfaces in metric Lie groups""""1. Introduction""; ""2. Lie groups and homogeneous three-manifolds""; ""3. Surface theory in three-dimensional metric Lie groups""; ""4. Open problems and unsolved conjectures for -surfaces in three-dimensional metric Lie groups""; ""References""; ""Stochastic methods for minimal surfaces""; ""1. Introduction""; ""2. Basic notions""; ""3. Parabolicity and area growth""; ""4. Coupling""; ""References""; ""The role of minimal surfaces in the study of the Allen-Cahn equation""; ""1. The role of minimal hypersurfaces""
""2. Entire solutions of the Allen-Cahn equation in Euclidean space""""3. Proof of Theorem 1.1""; ""References""; ""On curvature estimates for constant mean curvature surfaces""; ""Introduction""; ""1. Bounding ""; ""2. Schoen Curvature Estimate""; ""3. Choi-Schoen Curvature Estimate""; ""4. Colding-Minicozzi One-Sided Curvature Estimate""; ""5. Curvature Estimate For CMC Disks""; ""References""