Ulrich Dierkes & Stefan Hildebrandt 
Minimal Surfaces I [PDF ebook] 
Boundary Value Problems

Minimal surfaces I is an introduction to the field ofminimal surfaces and apresentation of the classical theoryas well as of parts of the modern development centeredaround boundary value problems. Part II deals with theboundary behaviour of minimal surfaces. Part I isparticularly apt for students who want to enter thisinteresting area of analysis and differential geometry whichduring the last 25 years of mathematical research has beenvery active and productive. Surveys of various subareas willlead the student to the current frontiers of knowledge andcan alsobe useful to the researcher. The lecturer caneasily base courses of one or two semesters on differentialgeometry on Vol. 1, as many topics are worked out in greatdetail. Numerous computer-generated illustrations of old andnew minimal surfaces are included to support intuition andimagination. Part 2 leads the reader up to the regularitytheory fornonlinear elliptic boundary value problemsillustrated by a particular and fascinating topic. There isno comparably comprehensive treatment of the problem ofboundary regularity of minimal surfaces available in bookform. This long-awaited book is a timely and welcomeaddition to the mathematical literature.