Memoirs of the American Mathematical Society 1994; 90 pp; softcover Volume: 108 ISBN10: 0821825828 ISBN13: 9780821825822 List Price: US$38 Individual Members: US$22.80 Institutional Members: US$30.40 Order Code: MEMO/108/520
 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 groundbreaking work of Brakke, combined with the recently developed "levelset" 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. Readership Geometric measure theorists as well as mathematicians involved in partial differential equations and phase transitions. Table of Contents  Elliptic regularization
 Partial regularity in codimension one
 Appendix
 References
