Minimal Surfaces of Codimension One

Umberto Massari and Mario Miranda (Eds.)0444868739, 9780444868732, 9780080872025

This book gives a unified presentation of different mathematical tools used to solve classical problems like Plateau’s problem, Bernstein’s problem, Dirichlet’s problem for the Minimal Surface Equation and the Capillary problem. The fundamental idea is a quite elementary geometrical definition of codimension one surfaces. The isoperimetric property of the Euclidean balls, together with the modern theory of partial differential equations are used to solve the 19th Hilbert problem. Also included is a modern mathematical treatment of capillary problems.

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Table of contents :
Content:
Edited by
Page iii

Copyright page
Page iv

Dedication
Page v

Preface
Pages vii-viii
U. Massari, M. Miranda

Introduction
Page xiii

Chapter One Differential Properties of Surfaces
Pages 1-42

Chapter Two Sets of Finite Perimeter and Minimal Boundaries
Pages 43-151

Chapter Three The Dirichlet Problem for the Minimal Surface Equation
Pages 152-216

Chapter Four Unbounded Solutions
Pages 217-231

Appendix
Page 232

References
Pages 233-240

Analytic Index
Pages 241-242

List of Symbols
Page 243