Description
Book SynopsisProvides an extensive introduction to a few of the most prominent extrinsic flows, namely the curve shortening flow, the mean curvature flow, the Gauss curvature flow, the inverse-mean curvature flow, and fully nonlinear flows of mean curvature and inverse-mean curvature type.
Trade ReviewThis textbook, written by four experts in the field, offers an authoritative introduction and overview to the topic of extrinsic geometric flows. It will serve well as a primary text for a graduate student who already has background knowledge of differential geometry and (some) partial differential equations. It will also serve as a useful reference for experts in the field."" - John Ross, Southwestern University
Table of Contents
- The heat equation
- Introduction to curve shortening
- The Gage-Hamilton-Grayson theorem
- Self-similar and ancient solutions
- Hypersurfaces in Euclidean space
- Introduction to mean curvature flow
- Mean curvature flow of entire graphs
- Huisken's theorem
- Mean convex mean curvature flow
- Monotonicity formulae
- Singularity analysis
- Noncollapsing
- Self-similar solutions
- Ancient solutions
- Gauss curvature flows
- The affine normal flow
- Flows by superaffine powers of the Gauss curvature
- Fully nonlinear curvature flows
- Flows of mean curvature type
- Flows of inverse-mean curvature type
- Bibliography
- Index
