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AMS/IP Studies in Advanced Mathematics

Volume 32

# Lectures on Mean Curvature Flow

Xi-Ping Zhu

Original Publication: 2002

Publisher: American Mathematical Society / International Press

Language: English

150 pages

## Description

'Mean curvature flow' is a term that is used to describe the evolution of a hyper surface whose normal velocity is given by the mean curvature. In the simplest case of a convex closed curve on the plane, the properties of the mean curvature flow are described by Gage-Hamilton's theorem. This theorem states that under the mean curvature flow, the curve collapses to a point, and if the flow is diluted so that the enclosed area equals $\pi$, the curve tends to the unit circle. In this book, the author gives a comprehensive account of fundamental results on singularities and the asymptotic behavior of mean curvature flows in higher dimensions.Among other topics, he considers in detail Huisken's theorem (a generalization of Gage-Hamilton's theorem to higher dimension), evolution of non-convex curves and hypersurfaces, and the classification of singularities of the mean curvature flow. Because of the importance of the mean curvature flow and its numerous applications in differential geometry and partial differential equations, as well as in engineering, chemistry, and biology, this book can be useful to graduate students and researchers working in these areas. The book would also make a nice supplementary text for an advanced course in differential geometry. Prerequisites include basic differential geometry, partial differential equations, and related applications.

## Publications

 Pub. Date ISBN-13 ISBN-10 Medium Binding Size, Etc. Status List Price 2017 Jan 9781470438210 1470438216 Print . electronic edition In Print 2002 9780821833117 0821833111 Print hardcover In Print US\$45.00