Lecture notes on mean curvature flow / Carlo Mantegazza
Type de document : Livre numériqueCollection : Progress in mathematics, 290Langue : anglais.Éditeur : Basel : Birkhäuser, cop. 2011ISBN: 9783034801447.ISSN: 0743-1643.Sujet MSC : 53-02, Research exposition (monographs, survey articles) pertaining to differential geometry53Exx, Differential geometry - Geometric evolution equations
35K55, PDEs - Parabolic equations and parabolic systems, Nonlinear parabolic equations
53C21, Global differential geometry, Methods of global Riemannian geometry, including PDE methods; curvature restrictionsEn-ligne : Springerlink | zbMath
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The first chapter is devoted to definitions, geometric properties and the first results and examples of the mean curvature flow. Chapter 2 centers around the maximum principle and its applications, in particular, to the behavior of the curvature at singularities. Chapter 3 is devoted to type-I singularities and the monotonicity formula of Huisken, while Chapter 4 is devoted to type-II singularities. In Chapter 5 some particular results are considered, including a detailed consideration of evolving curves in the plane. The book finishes with 6 appendices.
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