Plateau's Problem and the Calculus of Variations

Michael Struwe (Autor)

Buch | Hardcover

160 Seiten

2016
Princeton University Press (Verlag)
978-0-691-63627-6 (ISBN)

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This book is meant to give an account of recent developments in the theory of Plateau's problem for parametric minimal surfaces and surfaces of prescribed constant mean curvature ("H-surfaces") and its analytical framework. A comprehensive overview of the classical existence and regularity theory for disc-type minimal and H-surfaces is given and recent advances toward general structure theorems concerning the existence of multiple solutions are explored in full detail. The book focuses on the author's derivation of the Morse-inequalities and in particular the mountain-pass-lemma of Morse-Tompkins and Shiffman for minimal surfaces and the proof of the existence of large (unstable) H-surfaces (Rellich's conjecture) due to Brezis-Coron, Steffen, and the author. Many related results are covered as well. More than the geometric aspects of Plateau's problem (which have been exhaustively covered elsewhere), the author stresses the analytic side. The emphasis lies on the variational method. Originally published in 1989.
The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

*FrontMatter, pg. i*Contents, pg. vii*Preface, pg. ix*I. Existence of a solution, pg. 5*II. Unstable minimal surfaces, pg. 33*III. The existence of surfaces of prescribed constant mean curvature spanning a Jordan curve in IR3, pg. 91*IV. Unstable H-surfaces, pg. 111*References, pg. 141

Erscheinungsdatum	27.05.2016
Reihe/Serie	Princeton Legacy Library
Verlagsort	New Jersey
Sprache	englisch
Maße	152 x 229 mm
Gewicht	397 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
ISBN-10	0-691-63627-3 / 0691636273
ISBN-13	978-0-691-63627-6 / 9780691636276
Zustand	Neuware