Minimal Surfaces I

Beschreibung

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.
Vol. 1 provides an introduction to the classical theory of minimal surfaces in three-dimensional Euclidean space as well as a presentation of basic results on boundary value problems for minimal surfaces. Existence results are emphasized, but uniqueness and nonuniqueness questions, isoperimetric inequalities, geometric inclusion theorems and related topics are also dealt with. Surveys of important discoveries of the last 20 years lead the reader to the frontiers of present research. Vol. 2 presents a comprehensive study of the boundary behaviour of minimal surfaces. This is a fascinating part of the regularity theory for solutions of nonlinear elliptic boundary problems for systems of elliptic systems of partial differential equations.

Autor*in

Ulrich Dierkes

Themen in »Minimal Surfaces I«

Analysis Calculus of Variations Minimal Surfaces Minimal surface Nonlinear Boundary Value Problems Partial Differential Equations differential geometry

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