A Survey of Minimal Surfaces (Dover Books on Mathematics) by Robert Osserman (PDF)

Description

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.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐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 datedin it’s material. Robert Osserman is recognized as a great teacher of mathematicsby many in the mathematics community. But his approach has come betweenthe 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 paperpublishing. But I can see grad students rushing to resell this bookas it has a limited amount of useful reference informationand 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 thathelp in understanding the material not by theorem proving ,but by visualization and explanation that are needed.In that: this book fails. But compared to many other such mathematics books , it is actually superior!

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