Free Delivery Over $100
|
|
|||
|
||||
OverviewGeometric flows have many applications in physics and geometry. The mean curvature flow occurs in the description of the interface evolution in certain physical models. This is related to the property that such a flow is the gradient flow of the area functional and therefore appears naturally in problems where a surface energy is minimized. The mean curvature flow also has many geometric applications, in analogy with the Ricci flow of metrics on abstract riemannian manifolds. One can use this flow as a tool to obtain classification results for surfaces satisfying certain curvature conditions, as well as to construct minimal surfaces. Geometric flows, obtained from solutions of geometric parabolic equations, can be considered as an alternative tool to prove isoperimetric inequalities. On the other hand, isoperimetric inequalities can help in treating several aspects of convergence of these flows. Isoperimetric inequalities have many applications in other fields of geometry, like hyperbolic manifolds. Full Product DetailsAuthor: Manuel Ritoré , Vicente Miquel , Carlo Sinestrari , Joan PortiPublisher: Birkhauser Verlag AG Imprint: Birkhauser Verlag AG Edition: 2010 ed. Dimensions: Width: 17.00cm , Height: 1.00cm , Length: 24.40cm Weight: 0.454kg ISBN: 9783034602129ISBN 10: 303460212 Pages: 114 Publication Date: 19 October 2009 Audience: College/higher education , Postgraduate, Research & Scholarly Format: Paperback Publisher's Status: Active Availability: In Print  This item will be ordered in for you from one of our suppliers. Upon receipt, we will promptly dispatch it out to you. For in store availability, please contact us. Table of ContentsThe classical isoperimetric inequality in Euclidean space. Three different approaches.- The curve shortening flow and isoperimetric inequalities on surfaces.- $H^k$-flows and isoperimetric inequalities.- Estimates on the Willmore functional and isoperimetric inequalities.- Singularities in the volume-preserving mean curvature flow.- Bounds on the Heegaard genus of a hyperbolic manifold.- The isoperimetric profile for small volumes.- Local existence of flows driven by the second fundamental form and formation of singularities.- Invariance properties.- Singular behaviour of convex surfaces.- Convexity estimates.- Rescaling near a singularity.- Cylindrical and gradient estimates.- Mean curvature flow with surgeries.ReviewsAuthor InformationTab Content 6Author Website:Countries AvailableAll regions |
||||
