Plateau's Problem and the Calculus of Variations - Couverture rigide

Struwe, Michael

Couverture rigide

ISBN 10 : 0691636273 ISBN 13 : 9780691636276

Editeur : Princeton University Press, 2016

Synopsis

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.

A propos du livre

Présentation de l'éditeur

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 paperback editions preserve the original texts of these important books while presenting them in durable paperback 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.

Biographie de l'auteur

Michael Struwe is full Professor of Mathematics at ETH Zurich. Prof. Struwe was born on October 6, 1955 in Wuppertal, Germany. He studied mathematics at the University of Bonn. After receiving his doctorate in 1980, he was a member of the scientific staff in the special research sector 72 of the German research foundation and later an assistant at the Mathematical Institute of the University of Bonn. He spent extended research visits in Paris and at the ETH Zurich. In 1984 he was awarded the Felix Hausdorff Prize of the University of Bonn. On April 1, 1986 Michael Struwe was appointed assistant professor, on October 1, 1990 associate professor and in 1993 he became full Professor of Mathematics at the ETH Zurich. From October, 2002 to September, 2004 he served as head of the ETH Mathematics Department. His research focuses on non-linear partial differential equations and the calculus of variations as well as their applications in mathematical physics and differential geometry. In 2006 he received the Credit Suisse Award For Best Teaching. He is editor of the series A, A Lectures in Mathematics, ETH ZAA1/4richA, A and co-editor of the series A, AZurich Lectures in Advanced MathematicsA, A; moreover, he is co-editor of the journals A, ACalculus of VariationsA, A, A, ADuke Mathematical JournalA, A, and A, AInternational Mathematical Research NoticesA, A.

Détails de l'édition

• Éditeur: Princeton University Press
• Date d'édition: 2016
• Langue: anglais
• ISBN 10: 0691636273
• ISBN 13: 9780691636276
• Reliure: Relié
• Nombre de pages: 160
• Coordonnées du fabricant: non disponible