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Extrinsic Geometric Flows

By: Andrews, Ben Chow, Bennett Guenther, Christine Langford, Mat

Part of the Graduate Studies in Mathematics series
147045596X / 9781470455965
Published 30/05/2020
United States
178 x 254 mm 790 pages
Professional & Vocational  Learn More

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.


PBM Geometry, PBP Topology

Our price£80.81
RRP £97.95
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