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.
Most Helpful Customer Reviews
In my experience accessibility and understandability have to balance theorem proving. This book is well on it's way to becoming a modern classic even if it is somewhat dated in it's material. Robert Osserman is recognized as a great teacher of mathematics by many in the mathematics community. But his approach has come between the seeker of knowledge and his goal of understanding and mastery of the subject. It is not his fault as in a peer review he would be generally rewarded for his approach as he has been in his paper publishing. But I can see grad students rushing to resell this book as it has a limited amount of useful reference information and very few of the actual definitions of the curves talked about. The references are classic and many of the people are dead or retired by now. It is access to the actual formulations for the minimal surfaces and explanations that help in understanding the material not by theorem...
Osserman's survey is both an excellent starting point for beginners and a reference for some interesting problems in the subject (although it was written some years ago!). Weiesrtrass' classical representation of minimal surfaces, their topology...how can all these be in such a small book?
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