Geometric Analysis: Partial Differential Equations and Surfaces
About this Title
Joaquín Pérez, Universidad de Granada, Granada, Spain and José A. Gálvez, Universidad de Granada, Granada, Spain, Editors
Publication: Contemporary Mathematics
Publication Year 2012: Volume 570
ISBNs: 978-0-8218-4992-7 (print); 978-0-8218-8782-0 (online)
This volume contains research and expository articles from the courses and talks given at the RSME Lluis A. Santaló 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.
Graduate students and research mathematicians interested in differential geometry and partial differential geometry.
Table of Contents
- José A. Gálvez and Pablo Mira – Geometric PDEs in the presence of isolated singularities
- William H. Meeks III and Joaquín Pérez – Constant mean curvature surfaces in metric Lie groups
- Robert W. Neel – Stochastic methods for minimal surfaces
- Frank Pacard – The role of minimal surfaces in the study of the Allen-Cahn equation
- Giuseppe Tinaglia – On curvature estimates for constant mean curvature surfaces