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Lieferstatus:	Auf Bestellung (Lieferzeit unbekannt)
Veröffentlichung:	November 2012
Genre:	Schulbücher
	Analysis / B / Calculus of variations / Calculus of Variations and Optimal Control; Optimization / Calculus of Variations and Optimization / Complex analysis, complex variables / Differential & Riemannian geometry / Differential calculus & equations / Differential Geometry / Differentialrechnung und -gleichungen / Differentielle und Riemannsche Geometrie / Functions of a Complex Variable / Functions of complex variables / Komplexe Analysis, komplexe Variablen, Funktionentheorie / Mathematical physics / Mathematics and Statistics / Mathematische Physik / Optimization / Partial Differential Equations / Theoretical, Mathematical and Computational Physics mehr...
ISBN:	9783642265211
EAN-Code:	9783642265211
Verlag:	Springer EN
Einband:	Kartoniert
Sprache:	English
Serie:	#340 - Grundlehren der mathematischen Wissenschaften
Dimensionen:	H 235 mm / B 155 mm / D
Gewicht:	973 gr
Seiten:	623
Illustration:	XVII, 623 p. 68 illus., 6 illus. in color., schwarz-weiss Illustrationen, farbige Illustrationen
Zus. Info:	EUDR exemption - product or manufacturing materials placed on the market prior to 31.12.2025.
Bewertung:	Titel bewerten / Meinung schreiben

Inhalt:

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.