Regularity of Minimal Surfaces - 9783642265211

Description: Regularity of Minimal Surfaces Please note: this item is printed on demand and will take extra time before it can be dispatched to you (up to 20 working days). Author(s): Ulrich Dierkes, Albrecht Kuster, Stefan Hildebrandt, Anthony Tromba Format: Paperback Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG, Germany Imprint: Springer-Verlag Berlin and Heidelberg GmbH & Co. K ISBN-13: 9783642265211, 978-3642265211 Synopsis 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 Plateaus 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 Plateaus problem have no interior branch points.

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Book Title: Regularity of Minimal Surfaces

Number of Pages: 623 Pages

Publication Name: Regularity of Minimal Surfaces

Language: English

Publisher: Springer-Verlag Berlin AND Heidelberg Gmbh & Co. KG, Albrecht Kuster

Item Height: 235 mm

Subject: Mathematics, Physics

Publication Year: 2012

Type: Textbook

Item Weight: 973 g

Author: Stefan Hildebrandt, Anthony Tromba, Ulrich Dierkes

Item Width: 155 mm

Series: Grundlehren Der Mathematischen Wissenschaften

Format: Paperback