| 书目名称 | Lecture Notes on Mean Curvature Flow: Barriers and Singular Perturbations |
| 编辑 | Giovanni Bellettini |
| 视频video | |
| 概述 | Elementary introduction to mean curvature flow, including the short time existence result, using the signed distance function.Detailed study of minimal barriers and their regularizations for mean curv |
| 丛书名称 | Publications of the Scuola Normale Superiore |
| 图书封面 |  |
| 描述 | 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. |
| 出版日期 | Textbook 2013 |
| 关键词 | fattening; mean curvature flow; parabolic Allen-Cahn equation |
| 版次 | 1 |
| doi | https://doi.org/10.1007/978-88-7642-429-8 |
| isbn_softcover | 978-88-7642-428-1 |
| isbn_ebook | 978-88-7642-429-8Series ISSN 2239-1460 Series E-ISSN 2532-1668 |
| issn_series | 2239-1460 |
| copyright | Edizioni della Normale 2013 |
发表于 2025-3-21 18:21:20
