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Field name	Details
Dewey Class	516.36
Title	Mean Curvature Flow and Isoperimetric Inequalities ([Ebook]) / by Manuel Ritoré, Carlo Sinestrari.
Author	Ritoré, Manuel
Added Personal Name	Sinestrari, Carlo
Other name(s)	SpringerLink (Online service)
Publication	Basel : Birkhäuser , 2010.
Physical Details	: online resource.
Series	Advanced Courses in Mathematics CRM Barcelona, Centre de Recerca Matemática
ISBN	9783034602136
Summary Note	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.:
Contents note	Foreword -- I. Formation of Singularities in the Mean Curvature Flow - Geometry of hypersurfaces - 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 -- II. Geometric Flows, Isoperimetric Inequalities and Hyperbolic geometry - Classical isoperimetric inequality in Euclidean space - Surfaces - Higher dimensions - Some applications to hyperbolic geometry -- Bibliography.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users).
Internet Site	http://dx.doi.org/10.1007/978-3-0346-0213-6
Links to Related Works	Subject References: Differential Geometry . Global analysis . Global Analysis and Analysis on Manifolds . Global differential geometry . Mathematics . Authors: author . Ritoré, Manuel . Sinestrari, Carlo . Corporate Authors: SpringerLink (Online service) . Series: Advanced Courses in Mathematics CRM Barcelona, Centre de Recerca Matemática . Classification: 516.36 . 516.36 (DDC 23) .

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Mean Curvature Flow and Isoperimetric Inequalities

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