Elliptic regularization and partial regularity for motion by mean curvature
About this Title
Publication: Memoirs of the American Mathematical Society
Publication Year 1994: Volume 108, Number 520
ISBNs: 978-0-8218-2582-2 (print); 978-1-4704-0097-2 (online)
MathSciNet review: 1196160
MSC: Primary 49Q20; Secondary 53A10, 58E12
This monograph considers (singular) surfaces moving by mean curvature, combining tools of geometric measure theory with “viscosity solution” techniques. Employing the geometrically natural concept of “elliptic regularization”, Ilmanen establishes the existence of these surfaces. The ground-breaking work of Brakke, combined with the recently developed “level-set” approach, yields surfaces moving by mean curvature that are smooth almost everywhere. The methods developed here should form a foundation for further work in the field. This book is also noteworthy for its especially clear exposition and for an introductory chapter summarizing the key compactness theorems of geometric measure theory.
Geometric measure theorists as well as mathematicians involved in partial differential equations and phase transitions.
Table of Contents
- I. Elliptic regularization
- II. Partial regularity in codimension one