Title 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

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Description 1 online resource (viii, 185 pages) : illustrations Series Contemporary mathematics ; v. 570 Contemporary mathematics (American Mathematical Society) ; v. 570. Contents ""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"" Bibliography Includes bibliographical references Notes Print version record Subject Minimal surfaces -- Congresses Geometry, Differential -- Congresses Differential equations, Partial -- Asymptotic theory -- Congresses Differential equations, Partial -- Asymptotic theory Geometry, Differential Minimal surfaces Differential geometry -- Classical differential geometry -- Minimal surfaces, surfaces with prescribed mean curvature. Partial differential equations -- Qualitative properties of solutions -- Critical exponents. Partial differential equations -- Qualitative properties of solutions -- Asymptotic behavior of solutions. Partial differential equations -- Elliptic equations and systems -- Variational methods for second-order elliptic equations. Partial differential equations -- Elliptic equations and systems -- Boundary value problems for second-order elliptic equations. Partial differential equations -- Elliptic equations and systems -- Elliptic Monge-Ampère equations. Partial differential equations -- Elliptic equations and systems -- Nonlinear elliptic equations. Calculus of variations and optimal control; optimization -- Manifolds -- Minimal surfaces. Differential geometry -- Global differential geometry -- Immersions (minimal, prescribed curvature, tight, etc.) Differential geometry -- Global differential geometry -- Global surface theory (convex surfaces á la A.D. Aleksandrov) Genre/Form Conference papers and proceedings Form Electronic book Author Pérez, Joaquín, 1966- Galvez, José A., 1972- ISBN 9780821887820 0821887823

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