Global Analysis of Minimal Surfaces

• Main Authors: Dierkes, Ulrich. (Author), Hildebrandt, Stefan. (Author), Tromba, Anthony J. (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg, 2010.
• Series: Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics, 341
• Subjects: Mathematics.; Functions of complex variables.; Global analysis.; Differential equations, partial.; Global differential geometry.; Calculus of Variations and Optimal Control, Optimization.; Differential Geometry.; Partial Differential Equations.; Functions of a Complex Variable.; Theoretical, Mathematical and Computational Physics.; Global Analysis and Analysis on Manifolds.
• Online Access: https://ezaccess.library.uitm.edu.my/login?url=http://dx.doi.org/10.1007/978-3-642-11706-0

Many properties of minimal surfaces are of a global nature, and this is already true for the results treated in the first two volumes of the treatise. Part I of the present book can be viewed as an extension of these results. For instance, the first two chapters deal with existence, regularity and u...

Table of Contents:

• Introduction
• Part I. Free Boundaries and Bernstein Theorems
• 1.Minimal Surfaces with Supporting Half-Planes
• 2.Embedded Minimal Surfaces with Partially Free Boundaries
• 3.Bernstein Theorems and Related Results
• Part II. Global Analysis of Minimal Surfaces
• 4.The General Problem of Plateau: Another Approach
• 5.The Index Theorems for Minimal Surfaces of Zero and Higher Genus
• 6.Euler Characteristic and Morse Theory for Minimal Surfaces
• Bibliography
• Index.