Geometric analysis : partial differential equations and surfaces : UIMP-RSME Santaló Summer School geometric analysis, June 28-July 2, 2010, University of Granada, Granada, Spain / Joaquín Pérez, José A. Galvez, editors.

Format:

Book

Conference/Event

Author/Creator:

UIMP-RSME Santaló Summer School, Corporate Author.

Contributor:

Pérez, Joaquín, 1966- editor.

Galvez, José A., 1972- editor.

Conference Name:

UIMP-RSME Santaló Summer School (2010 : University of Granada), issuing body.

UIMP-RSME Santalâo Summer School

Series:

Contemporary mathematics (American Mathematical Society). 0271-4132 0271-4132 570

Contemporary mathematics, 570 0271-4132 0271-4132

Language:

English

Subjects (All):

Minimal surfaces--Congresses.

Minimal surfaces.

Geometry, Differential--Congresses.

Geometry, Differential.

Differential equations, Partial--Asymptotic theory--Congresses.

Differential equations, Partial.

Physical Description:

1 online resource (198 p.)

Edition:

1st ed.

Place of Publication:

Providence, Rhode Island : American Mathematical Society, [2012]

Language Note:

English

Summary:

This volume contains research and expository articles from the courses and talks given at the RSME Lluis A. Santalo Summer School, ``Geometric Analysis'', held June 28-July 2, 2010, in Granada, Spain. The goal of the Summer School was to present some of the many advances currently taking place in the interaction between partial differential equations and differential geometry, with special emphasis on the theory of minimal surfaces. This volume includes expository articles about the current state of specific problems involving curvature and partial differential equations, with interactions to neighboring fields such as probability. An introductory, mostly self-contained course on constant mean curvature surfaces in Lie groups equipped with a left invariant metric is provided. The volume will be of interest to researchers, post-docs, and advanced PhD students in the interface between partial differential equations and differential geometry. This book is published in cooperation with Real Sociedad Matematica Espanola (RSME).

Contents:

Preface

Geometric PDEs in the presence of isolated singularities

1. Introduction

2. The Hessian one equation: preliminaries

3. Isolated singularities of - local study

4. Isolated singularities of - 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

9. Further results and open problems

References

Constant mean curvature surfaces in metric Lie groups

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

Stochastic methods for minimal surfaces

2. Basic notions

3. Parabolicity and area growth

4. Coupling

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

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.

Notes:

Description based upon print version of record.

Includes bibliographical references.

Description based on print version record.

ISBN:

0-8218-8782-3