A Theory of Branched Minimal Surfaces
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A Theory of Branched Minimal Surfaces

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ISBN-13:
9783642256202
Einband:
eBook
Seiten:
194
Autor:
Anthony Tromba
Serie:
Schriftenreihe Markt und Marketing Springer Monographs in Mathematics
eBook Typ:
PDF
eBook Format:
EPUB
Kopierschutz:
1 - PDF Watermark
Sprache:
Englisch
Beschreibung:

This book shows how to calculate arbitrarily high orders of derivatives of the Douglas Energy defined on the infinite dimensional manifold of all surfaces spanning a contour, breaking new ground in the Calculus of Variations.

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.¿
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.