Minimal Surfaces of Codimension OneElsevier, Apr 1, 2000 - 242 pages 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. |
Contents
| 1 | |
CHAPTER TWO SETS OF FINITE PERIMETER AND MINIMAL BOUNDARIES | 43 |
CHAPTER THREE THE DIRICHLET PROBLEM FOR THE MINIMAL SURFACE EQUATION | 152 |
CHAPTER FOUR UNBOUNDED SOLUTIONS | 217 |
Appendix | 232 |
References | 233 |
| 241 | |
List of symbols | 243 |
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Common terms and phrases
analytic argument assume ball Bernstein bounded chapter choose classical closed compact condition consequence consider constant contained continuous converges convex defined denote derivatives differential Dirichlet problem dist easily equal estimate exists fact fixed function Giorgi give given gradu graph holds identity implies increasing inequality integral interesting isoperimetric Lemma Lipschitz function Math meas measurable sets minimal boundary minimal cone minimal surface equation negative observe obtain obviously open set positive present problem PROOF Proposition prove Radon measures recalling remark respect result satisfies sequence singular smoothness ſº solution strictly subset sufficient THEOREM unique values variation vector write