| 书目名称 | Global Analysis of Minimal Surfaces | | 编辑 | Ulrich Dierkes,Stefan Hildebrandt,Anthony J. Tromb | | 视频video | | | 概述 | Together with vol..340 it is the long expected 2nd edition of the Grundlehren vol..First part is the extension of the results treated in volumes 339 and 340 Second Part contains a "global theory of mi | | 丛书名称 | Grundlehren der mathematischen Wissenschaften | | 图书封面 |  | | 描述 | Many properties of minimal surfaces are of a global nature, and this is already true for the results treated in the first two volumes of the treatise. Part I of the present book can be viewed as an extension of these results. For instance, the first two chapters deal with existence, regularity and uniqueness theorems for minimal surfaces with partially free boundaries. Here one of the main features is the possibility of "edge-crawling" along free parts of the boundary.The third chapter deals with a priori estimates for minimal surfaces in higher dimensions and for minimizers of singular integrals related to the area functional. In particular, far reaching Bernstein theorems are derived.The second part of the book contains what one might justly call a "global theory of minimal surfaces" as envisioned by Smale. First, the Douglas problem is treated anew by using Teichmüller theory. Secondly, various index theorems for minimal theorems are derived, and their consequences for the space of solutions to Plateau´s problem are discussed. Finally, a topological approach to minimal surfaces via Fredholm vector fields in the spirit of Smale is presented. | | 出版日期 | Book 1992Latest edition | | 关键词 | 49Q05,53A05, 53A07, 53B20, 35J20, 35J47, 35J50, 35J75, 49Q20; calculus of variations; conformal mappin | | 版次 | 2 | | doi | https://doi.org/10.1007/978-3-642-11706-0 | | isbn_softcover | 978-3-642-26533-4 | | isbn_ebook | 978-3-642-11706-0Series ISSN 0072-7830 Series E-ISSN 2196-9701 | | issn_series | 0072-7830 | | copyright | Springer-Verlag Berlin Heidelberg 1992 |
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发表于 2025-3-21 17:38:02
