Overview
Part of the book series: Grundlehren der mathematischen Wissenschaften (GL, volume 339-341)
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Keywords
- 49Q05,53A05, 53A07, 53B20, 35J20, 35J47, 35J50, 35J75, 49Q20
- calculus of variations
- conformal mappings
- differential geometry
- minimal surfaces
- regularity theory
- partial differential equations
About this book
The three-volume treatise consists of the volumes Minimal Surfaces (GL 339), Regularity of Minimal Surfaces (GL 340), and Glolbal Theory of Minimal Surfaces (GL 341) that replace the monograph Minimal Surfaces I , II, published as volumes 295 and 296 of the Grundlehren der mathematischen Wissenschaft series.
Ther first volume covers the classical theory as well as existence results concerning boundary value problems for minimal surfaces, in particular results for Plateau's problem.
The second volume deals with basic regularity results for minimal surfaces concerning their boundary behaviour at Plateau boundaries and free boundaries. Moreover, exclosure theorems, isoperimetricc inequalities and existence theorems for surfaces of prescribed mean curvature in a Riemanian manifold and for the thread problem are discussed.
Finally, the third volume deals with geometric properties of minimal surfaces with free boundaries and with a priori gradient estimates for n-dimensional minimal surfaces, leading to various Bernstein-type theorems. Secondly, a global theory of minimal surfaces (as envisioned by Smale) is presented, including index theorems.
Authors and Affiliations
Bibliographic Information
Book Title: Minimal Surfaces
Authors: Ulrich Dierkes, Stefan Hildebrandt, Friedrich Sauvigny, Anthony Tromba
Series Title: Grundlehren der mathematischen Wissenschaften
Publisher: Springer Berlin, Heidelberg
Copyright Information: Springer-Verlag Berlin Heidelberg 2011
Series ISSN: 0072-7830
Series E-ISSN: 2196-9701
Edition Number: 2
Number of Pages: L, 1910
Additional Information: Originally published as volumes 295 and 296 in series: Grundlehren der mathematischen Wissenschaft series