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Titlebook: Global Analysis of Minimal Surfaces; Ulrich Dierkes,Stefan Hildebrandt,Anthony J. Tromb Book 1992Latest edition Springer-Verlag Berlin Hei

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書目名稱Global Analysis of Minimal Surfaces
編輯Ulrich Dierkes,Stefan Hildebrandt,Anthony J. Tromb
視頻videohttp://file.papertrans.cn/387/386010/386010.mp4
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
叢書名稱Grundlehren der mathematischen Wissenschaften
圖書封面Titlebook: Global Analysis of Minimal Surfaces; Ulrich Dierkes,Stefan Hildebrandt,Anthony J. Tromb Book 1992Latest edition Springer-Verlag Berlin Hei
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
關(guān)鍵詞49Q05,53A05, 53A07, 53B20, 35J20, 35J47, 35J50, 35J75, 49Q20; calculus of variations; conformal mappin
版次2
doihttps://doi.org/10.1007/978-3-642-11706-0
isbn_softcover978-3-642-26533-4
isbn_ebook978-3-642-11706-0Series ISSN 0072-7830 Series E-ISSN 2196-9701
issn_series 0072-7830
copyrightSpringer-Verlag Berlin Heidelberg 1992
The information of publication is updating

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The General Problem of Plateau: Another Approachned and some of the principal existence results due to Douglas, Courant, and Shiffman are stated. Finally, the general Plateau problem for orientable surfaces is handled in combination with an obstacle problem in order to obtain a sufficient condition for the solvability of the general Douglas–Plate
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https://doi.org/10.1007/978-1-4684-8712-1ned and some of the principal existence results due to Douglas, Courant, and Shiffman are stated. Finally, the general Plateau problem for orientable surfaces is handled in combination with an obstacle problem in order to obtain a sufficient condition for the solvability of the general Douglas–Plate
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https://doi.org/10.1007/978-1-349-00879-7hese ideas are applied to sufficiently smooth embeddings .:..→?. realizing a closed Jordan curve .=.(..). This leads to the definition of gradient vector fields . defined on the homotopically nontrivial component . of sufficiently smooth mappings ..→., where . is the parameter domain, such that the
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0072-7830 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.978-3-642-26533-4978-3-642-11706-0Series ISSN 0072-7830 Series E-ISSN 2196-9701
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