A Survey of Minimal Surfaces (Dover Books on Mathematics)

Clear and comprehensive, this examination of minimal surfaces features twelve sections that discuss parametric and non-parametric surfaces, surfaces that minimize area, isothermal parameters on surfaces, Bernstein's theorem, minimal surfaces with boundary, and many other topics.
This edition features substantial revisions and additions to the original work, including the uses of minimal surfaces to settle important conjectures in relativity and topology. Other enlargements include updated work on Plateau's problem and isoperimetric inequalities as well as a new appendix, supplementary references, and expanded indexes.

Robert Osserman (1926–2011) was Professor of Mathematics at Stanford University. His other Dover book is Two-Dimensional Calculus.