Minimal surfaces I is an introduction to the field of minimal surfaces and apresentation of the classical theory as well as of parts of the modern development centered around boundary value problems. Part II deals with the boundary behaviour of minimal surfaces. Part I is particularly apt for students who want to enter this interesting area of analysis and differential geometry which during the last 25 years of mathematical research has been very active and productive. Surveys of various subareas will lead the student to the current frontiers of knowledge and can alsobe useful to the researcher. The lecturer can easily base courses of one or two semesters on differential geometry on Vol. 1, as many topics are worked out in great detail. Numerous computer-generated illustrations of old and new minimal surfaces are included to support intuition and imagination. Part 2 leads the reader up to the regularity theory fornonlinear elliptic boundary value problems illustrated by a particular and fascinating topic. There is no comparably comprehensive treatment of the problem of boundary regularity of minimal surfaces available in book form. This long-awaited book is a timely and welcome addition to the mathematical literature.
This has in detail been carried out by P. Dombrowski [1]. Remark 2. Consider the nonparametric surface which is given as graph of a function p(x, y), (x, y) e Q C R*. We can embed z = p(x, y) into the family of surfaces 2 = p(x,y) + c ...
This book starts with the classical theory of minimal surfaces and ends up with current research topics.
F. Tomi and A. J. Tromba 1. Extreme curves bound an embedded minimal surface of the disk type, Math. Z., 158 (1978), 137-145. A. J. Tromba 1. On the number of simply connected minimal surfaces spanning a curve, Mem. Amer. Math.
... 1905 (cf. also Dombrowski [2], and General investigations of curved surfaces. Raven Press, New York, 1965) Gergonne, J.D. 1. Questions proposées/résolues. Ann. Math. Pure Appl. 7, 68, 99–100, 156, 143–147 (1816) Gerhardt, C. 1.
1985, D. Hoffman and W. Meeks, [HoMe1], proved that Costa's surface was embedded; this surface is now known as the Costa-Hoffman-Meeks surface. Moreover, Hoffman and Meeks showed that Costa's surface was just the first in a family of ...
Minimal Surfaces is the first volume of a three volume treatise on minimal surfaces (Grundlehren Nr. 339-341).
Kluwer Academic Publishers Group, Dordrecht, 1989. Translated from the Russian by R. A. M. Hoksbergen. 89. K. Cieliebak and Y. Eliashberg. From Stein to Weinstein and back. Symplectic geometry of affine complex manifolds, ...
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.
Minimal Surfaces
278-279, 289–290, 293, 365,423 Darboux, G. 52, 133, 135, 149, 194, 277 Davids, N. 365 De Giorgi, E. 86, 284 Dierkes, U. 292; 87,278, 424–426 Do Carmo, M. 48, 88 Dombrowski, P. 52, 80 Douglas, J. 9,340; 221, 277 Dubrovin, B. A. 48 Dziuk, ...