Lectures on Mean Curvature Flows (Ams/Ip Studies in Advanced Mathematics)
|Rating||:||4.98 (513 Votes)|
|Number of Pages||:||150 Pages|
'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. The book would also make a nice supplementary text for an advanced course in differential geometry. 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. 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 c
Five Stars Thomas R. Schulte Excellent book and excellent service!