Minimal Surfaces of Codimension One ( Volume 91 )

Publication series ：Volume 91

Author： Massari U.;Miranda M.

Publisher： Elsevier Science‎

Publication year： 2000

E-ISBN: 9780080872025

P-ISBN(Paperback): 9780444868732

P-ISBN(Hardback): 9780444868732

Subject： O186 Differential Geometry and Integral Geometry

Language： ENG

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Description

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.

Chapter

Front Cover

pp.： 1 – 4

Minimal Surfaces of Codimension One

pp.： 4 – 5

pp.： 5 – 10

Preface

pp.： 9 – 14

Contents

pp.： 10 – 9

Introduction

pp.： 14 – 16

CHAPTER ONE. DIFFERENTIAL PROPERTIES OF SURFACES

pp.： 16 – 58

CHAPTER TWO. SETS OF FINITE PERIMETER AND MINIMAL BOUNDARIES

pp.： 58 – 167

CHAPTER THREE. THE DIRICHLET PROBLEM FOR THE MINIMAL SURFACE EQUATION

pp.： 167 – 232

CHAPTER FOUR. UNBOUNDED SOLUTIONS

pp.： 232 – 247

Appendix

pp.： 247 – 248

References

pp.： 248 – 256

Analytic index

pp.： 256 – 258

List of symbols

pp.： 258 – 260

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