Minimal Surfaces

2., rev. and enlarged Auflage 2011
ISBN: 978-3-642-11715-2
Verlag: Springer

Buch, Englisch, Band 339-341, 1910 Seiten

Reihe: Grundlehren der mathematischen Wissenschaften

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.

Zielgruppe

Research

Autoren/Hrsg.

Dierkes, Ulrich

Hildebrandt, Stefan

Sauvigny, Friedrich

Tromba, Anthony

Weitere Mitwirkende

Jakob, Ruben

Küster, Albrecht

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen
• Mathematik | Informatik Mathematik Geometrie Differentialgeometrie