---

＜電子ブック＞
Mean Curvature Flow and Isoperimetric Inequalities / by Manuel Ritoré, Carlo Sinestrari ; edited by Vicente Miquel, Joan Porti
(Advanced Courses in Mathematics - CRM Barcelona. ISSN:22970312)

版	1st ed. 2010.
出版者	(Basel : Birkhäuser Basel : Imprint: Birkhäuser)
出版年	2010
本文言語	英語
大きさ	VIII, 114 p : online resource
著者標目	*Ritoré, Manuel author Sinestrari, Carlo author Miquel, Vicente editor Porti, Joan editor SpringerLink (Online service)
件　名	LCSH:Geometry, Differential LCSH:Global analysis (Mathematics) LCSH:Manifolds (Mathematics) FREE:Differential Geometry FREE:Global Analysis and Analysis on Manifolds
一般注記	Formation of Singularities in the Mean Curvature Flow -- Geometry of hypersurfaces -- Examples -- Local existence and formation of singularities -- Invariance properties -- Singular behaviour of convex surfaces -- Convexity estimates -- Rescaling near a singularity -- Huisken’s monotonicity formula -- Cylindrical and gradient estimates -- Mean curvature flow with surgeries -- Geometric Flows, Isoperimetric Inequalities and Hyperbolic Geometry -- The classical isoperimetric inequality in Euclidean space -- Surfaces -- Higher dimensions -- Some applications to hyperbolic geometry Geometric 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 HTTP:URL=https://doi.org/10.1007/978-3-0346-0213-6

 類似資料