Minimal Surfaces I: Boundary Value Problems

"Minimal Surfaces 1" is an introduction to the field of minimal surfaces and a presentation of the classical theory as well as of parts of the modern development. Part 1 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 also be useful to the researcher. The lecturer can easily base courses of one or two semesters on differential geometry on Part 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.