A Theory of Branched Minimal Surfaces

• Main Author: Tromba, Anthony (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg, 2012.
• Series: Springer Monographs in Mathematics,
• Subjects: Mathematics.; Functions of complex variables.; Global analysis (Mathematics).; Manifolds (Mathematics).; Sequences (Mathematics).; Differential geometry.; Functions of a Complex Variable.; Sequences, Series, Summability.; Differential Geometry.; Global Analysis and Analysis on Manifolds.

One of the most elementary questions in mathematics is whether an area minimizing surface spanning a contour in three space is immersed or not; i.e. does its derivative have maximal rank everywhere. The purpose of this monograph is to present an elementary proof of this very fundamental and beautifu...

Table of Contents:

• 1.Introduction
• 2.Higher order Derivatives of Dirichlets' Energy
• 3.Very Special Case; The Theorem for n + 1 Even and m + 1 Odd
• 4.The First Main Theorem; Non-Exceptional Branch Points
• 5.The Second Main Theorem: Exceptional Branch Points; The Condition k > l
• 6.Exceptional Branch Points Without The Condition k > l
• 7.New Brief Proofs of the Gulliver-Osserman-Royden Theorem
• 8.Boundary Branch Points
• Scholia
• Appendix
• Bibliography.