Description

Book Synopsis
Provides 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 Review
This 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

    Extrinsic Geometric Flows

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      A Paperback / softback by Ben Andrews, Bennett Chow, Christine Guenther

      £77.40

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      RRP £86.00 – you save £8.60 (10%)

      Order before 4pm today for delivery by Mon 21 Sep 2026.

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        Book details

        Publisher American Mathematical Society
        Published 30 March 2020
        ISBN-13 9781470464578
        978-1470464578
        ISBN-10 1470464578
        Also in:
        Topology

        Description

        Book Synopsis
        Provides 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 Review
        This 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

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