Minimal Surfaces I / Grundlehren der mathematischen Wissenschaften Bd.295 (PDF)

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.