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.

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Yes, you can access Extrinsic Geometric Flows by Ben Andrews, Bennett Chow, Christine Guenther, Mat Langford in PDF and/or ePUB format, as well as other popular books in Mathematics & Mathematics General. We have over one million books available in our catalogue for you to explore.

Information

Publisher

American Mathematical Society

Year

2020

ISBN

9781470456863

Topic

Mathematics

Subtopic

Mathematics General

Index

Mathematics

Cover
Title page
Preface
A Guide for the Reader
Suggested Course Outlines
Notation and Symbols
Chapter 1. The Heat Equation
Chapter 2. Introduction to Curve Shortening
Chapter 3. The Gage–Hamilton–Grayson Theorem
Chapter 4. Self-Similar and Ancient Solutions
Chapter 5. Hypersurfaces in Euclidean Space
Chapter 6. Introduction to Mean Curvature Flow
Chapter 7. Mean Curvature Flow of Entire Graphs
Chapter 8. Huisken’s Theorem
Chapter 9. Mean Convex Mean Curvature Flow
Chapter 10. Monotonicity Formulae
Chapter 11. Singularity Analysis
Chapter 12. Noncollapsing
Chapter 13. Self-Similar Solutions
Chapter 14. Ancient Solutions
Chapter 15. Gauß Curvature Flows
Chapter 16. The Affine Normal Flow
Chapter 17. Flows by Superaffine Powers of the Gauß Curvature
Chapter 18. Fully Nonlinear Curvature Flows
Chapter 19. Flows of Mean Curvature Type
Chapter 20. Flows of Inverse-Mean Curvature Type
Bibliography
Index
Back Cover