Extrinsic Geometric Flows (Graduate Studies in Mathematics) - Hardcover

Ben Andrews; Bennett Chow; Christine Guenther; Mat Langford

Hardcover

ISBN 10: 147045596X ISBN 13: 9781470455965

Publisher: American Mathematical Society, 2020

Synopsis

Extrinsic geometric flows are characterized by a submanifold evolving in an ambient space with velocity determined by its extrinsic curvature. The goal of this book is to give 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. The authors highlight techniques and behaviors that frequently arise in the study of these (and other) flows. To illustrate the broad applicability of the techniques developed, they also consider general classes of fully nonlinear curvature flows. The book is written at the level of a graduate student who has had a basic course in differential geometry and has some familiarity with partial differential equations. It is intended also to be useful as a reference for specialists. In general, the authors provide detailed proofs, although for some more specialized results they may only present the main ideas; in such cases, they provide references for complete proofs. A brief survey of additional topics, with extensive references, can be found in the notes and commentary at the end of each chapter.

About this title

About the Author

Ben Andrews: The Australian National University, Canberra, Australia, Bennett Chow: University of California, San Diego, La Jolla, CA, Christine Guenther: Pacific University, Forest Grove, OR, Mat Langford: University of Tennessee, Knoxville, TN

Edition details

• Publisher: American Mathematical Society
• Publication date: 2020
• Language: English
• ISBN 10: 147045596X
• ISBN 13: 9781470455965
• Binding: Hardcover
• Number of pages: 790