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Titlebook: Regularity of Minimal Surfaces; Ulrich Dierkes,Stefan Hildebrandt,Anthony J. Tromb Book 2010Latest edition Springer-Verlag Berlin Heidelbe

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书目名称Regularity of Minimal Surfaces
编辑Ulrich Dierkes,Stefan Hildebrandt,Anthony J. Tromb
视频videohttp://file.papertrans.cn/826/825564/825564.mp4
概述together with vol..341 it is the expected 2nd edition of the Grundlehren vol..296 -discusses geometric properties of minimal and H-surfaces -includes a new approach to the Osserman-Gulliver-Alt theore
丛书名称Grundlehren der mathematischen Wissenschaften
图书封面Titlebook: Regularity of Minimal Surfaces; Ulrich Dierkes,Stefan Hildebrandt,Anthony J. Tromb Book 2010Latest edition Springer-Verlag Berlin Heidelbe
描述Regularity of Minimal Surfaces begins with a survey of minimal surfaces with free boundaries. Following this, the basic results concerning the boundary behaviour of minimal surfaces and H-surfaces with fixed or free boundaries are studied. In particular, the asymptotic expansions at interior and boundary branch points are derived, leading to general Gauss-Bonnet formulas. Furthermore, gradient estimates and asymptotic expansions for minimal surfaces with only piecewise smooth boundaries are obtained. One of the main features of free boundary value problems for minimal surfaces is that, for principal reasons, it is impossible to derive a priori estimates. Therefore regularity proofs for non-minimizers have to be based on indirect reasoning using monotonicity formulas.This is followed by a long chapter discussing geometric properties of minimal and H-surfaces such as enclosure theorems and isoperimetric inequalities, leading to the discussion of obstacle problems and of Plateau´s problem for H-surfaces in a Riemannian manifold.A natural generalization of the isoperimetric problem is the so-called thread problem, dealing with minimal surfaces whose boundary consists of a fixed arc of
出版日期Book 2010Latest edition
关键词Boundary value problem; Minimal surface; Riemannian manifold; calculus of variations; conformal mappings
版次2
doihttps://doi.org/10.1007/978-3-642-11700-8
isbn_softcover978-3-642-26521-1
isbn_ebook978-3-642-11700-8Series ISSN 0072-7830 Series E-ISSN 2196-9701
issn_series 0072-7830
copyrightSpringer-Verlag Berlin Heidelberg 2010
The information of publication is updating

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Branch Pointsibited which furnish bounds for the index of interior and boundary branch points. These estimates supplement the bounds on the order of branch points provided by the Gauss–Bonnet theorem..A special role in all of this is played by the . discovered by Böhme and Tromba, which will again show up in the global theory presented in Vol. 3.
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Enclosure and Existence Theorems for Minimal Surfaces and ,-Surfaces. Isoperimetric Inequalitiesns are the fundament for results ensuring the existence of minimal surfaces and .-surfaces solving Plateau’s problem in Euclidean space or in a Riemannian manifold respectively. Of particular interest in this context are ...In addition, . for minimal surfaces solving either Plateau’s problem or a free boundary problem are derived.
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0072-7830 -includes a new approach to the Osserman-Gulliver-Alt theoreRegularity of Minimal Surfaces begins with a survey of minimal surfaces with free boundaries. Following this, the basic results concerning the boundary behaviour of minimal surfaces and H-surfaces with fixed or free boundaries are studied.
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Minimal Surfaces with Free Boundariesg the direct methods of the calculus of variations, thus establishing the existence of minimizers with a boundary on a given supporting surface .. However, this method does not yield the existence of stationary minimal surfaces which are not area minimizing. The remaining part of the chapter deals w
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Singular Boundary Points of Minimal Surfacesis problem is the . which yields asymptotic expansions for complex-valued solutions .(.) of a differential inequality . at the center .=0 of a disk ..(0)={.∈ℂ:|.|<.}, and more general, of expansions for vector-valued solutions .(.) of a differential inequality . Such expansions are used in the prece
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