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 ...
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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.
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Add this copy of Regularity of Minimal Surfaces (Grundlehren Der to cart. $104.00, very good condition, Sold by BookHouse On-Line rated 5.0 out of 5 stars, ships from Minneapolis, MN, UNITED STATES, published 2010 by Springer.
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Very Good. No Dust Jacket. Size: 9x6x1; Binding tight and sturdy, text very good, prev owner's name. Very light shelfwear. NOT ex-lib. Due to the size/weight of this book extra charges may apply for international shipping. Ships from Dinkytown in Minneapolis, Minnesota.
Add this copy of Regularity of Minimal Surfaces to cart. $168.69, new condition, Sold by Ingram Customer Returns Center rated 5.0 out of 5 stars, ships from NV, USA, published 2010 by Springer.
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New. Print on demand Sewn binding. Paper over boards. 623 p. Contains: Unspecified, Illustrations, black & white, Illustrations, color, Frontispiece, Figures. Grundlehren Der Mathematischen Wissenschaften, 340.
