Regularity of Minimal Surfaces

Regularity of Minimal Surfaces

EnglishPaperback / softbackPrint on demand
Dierkes Ulrich
Springer, Berlin
EAN: 9783642265211
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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 given length. Existence and regularity of solutions are discussed. The final chapter on branch points presents a new approach to the theorem that area minimizing solutions of Plateau´s problem have no interior branch points.
EAN 9783642265211
ISBN 3642265219
Binding Paperback / softback
Publisher Springer, Berlin
Publication date November 5, 2012
Pages 623
Language English
Dimensions 235 x 155
Country Germany
Readership Professional & Scholarly
Authors Dierkes Ulrich; Hildebrandt, Stefan; Tromba Anthony
Illustrations XVII, 623 p. 68 illus., 6 illus. in color.
Edition Softcover reprint of hardcover 2nd ed. 2010
Series Grundlehren der mathematischen Wissenschaften
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