Lecture notes on mean curvature flow , barriers and singular perturbations [electronic resource]
- 作者： Bellettini, Giovanni.
- 其他作者：
- 其他題名：
- Appunti ;
- 出版： Pisa : Scuola Normale Superiore :Imprint: Edizioni della Normale
- 叢書名： Appunti / Scuola Normale Superiore ;12
- 主題： Curvature. , Flows (Differentiable dynamical systems) , Mathematics. , Geometry.
- ISBN： 9788876424298 (electronic bk.) 、 9788876424281 (paper)
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FIND@SFXID:
CGU
- 資料類型: 電子書
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讀者標籤：
- 系統號： 005395568 | 機讀編目格式
館藏資訊
The aim of the book is to study some aspects of geometric evolutions, such as mean curvature flow and anisotropic mean curvature flow of hypersurfaces. We analyze the origin of such flows and their geometric and variational nature. Some of the most important aspects of mean curvature flow are described, such as the comparison principle and its use in the definition of suitable weak solutions. The anisotropic evolutions, which can be considered as a generalization of mean curvature flow, are studied from the view point of Finsler geometry. Concerning singular perturbations, we discuss the convergence of the Allen–Cahn (or Ginsburg–Landau) type equations to (possibly anisotropic) mean curvature flow before the onset of singularities in the limit problem. We study such kinds of asymptotic problems also in the static case, showing convergence to prescribed curvature-type problems.