Regularity of Minimal Surfaces by Ulrich Dierkes
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.-
Complex Abelian Varieties
-
Entire Functions of Several Complex Variables
-
Finite Groups I
-
Markov Processes
-
Random Perturbations of Dynamical Systems
-
Global Analysis of Minimal Surfaces
-
Vorlesungen über Differenzenrechnung
-
Minimal Surfaces
-
Vorlesungen uber Topologie
-
Harmonic Analysis on Semi-Simple Lie Groups II
-
Einleitung in die Mengenlehre
-
Lagerungen in der Ebene auf der Kugel und im Raum
-
Algebraic Systems
-
Continuous Transformations in Analysis
-
Aufgaben und Lehrsätze aus der Analysis
-
Die Grundlagen der Quantenmechanik
-
Anfangswertprobleme bei Partiellen Differentialgleichungen
-
Foundations of the Mathematical Theory of Electromagnetic Waves
-
Equations Differentielles Operationnelles
-
Topology and Geometry of Intersections of Ellipsoids in R^n
-
Die Gruppentheoretische Methode in der Quantenmechanik
-
Theta Functions
-
Markov Processes, Structure and Asymptotic Behavior
-
Non-Homogeneous Boundary Value Problems and Applications
-
Endliche Gruppen I
-
Reelle Funktionen
-
Topological Vector Spaces II
-
An Introduction to the Theory of Multipliers
-
Baer *-Rings
-
Classification Theory of Riemann Surfaces
-
Best Approximation in Normed Linear Spaces by Elements of Linear Subspaces
-
Harmonic Analysis on Semi-Simple Lie Groups I
-
Moderne Algebra
-
Die Grundlagen der Theorie der Markoffschen Prozesse
-
Nevanlinna Theory in Several Complex Variables and Diophantine Approximation
-
Der Absolute Differentialkalkül und seine Anwendungen in Geometrie und Physik
-
Abstract Harmonic Analysis
-
Quasikonforme Abbildungen
-
Vorlesungen über Himmelsmechanik
-
Methoden der Mathematischen Physik
-
Analytische Dynamik der Punkte und Starren Körper
-
Grundprobleme der Mathematischen Theorie Elektromagnetischer Schwingungen
-
Vorlesungen über Differentialgeometrie und geometrische Grundlagen von Einsteins Relativitätstheorie I
From the reviews of the second edition:
“The most complete and thorough record of the ongoing efforts to justify Lagrange’s optimism… contain a wealth of new material in the form of newly written chapters and sections … . a compilation of results and proofs from a vast subject. Here were true scholars in the best sense of the word at work, creating their literary lifetime achievements. They wrote with love for detail, clarity and history, which makes them a pleasure to read. … will become instantaneous classics.” (Matthias Weber, The Mathematical Association of America, June, 2011)
| SKU | Unavailable |
| ISBN 13 | 9783642265211 |
| ISBN 10 | 3642265219 |
| Title | Regularity of Minimal Surfaces |
| Author | Ulrich Dierkes |
| Series | Grundlehren Der Mathematischen Wissenschaften |
| Condition | Unavailable |
| Binding Type | Paperback |
| Publisher | Springer |
| Year published | 2012-11-05 |
| Number of pages | 623 |
| Cover note | Book picture is for illustrative purposes only, actual binding, cover or edition may vary. |
| Note | Unavailable |