Plateau's Problem - An Invitation to Varifold Geometry - Frederick J. Almgren, Kenneth A. Brakke, John M. Sullivan (2001)
ISBN 9780821827475
Subject Differential topology; Minimal surfaces; Plateau's problem
Publisher American Mathematical Society
Publication Date 2001
Format Paperback (211 x 140 mm)
Language eng
Illustrator Kenneth A. Brakke
Illustrator John M. Sullivan
There have been many wonderful developments in the theory of minimal surfaces and geometric measure theory in the past 25 to 30 years. Many of the researchers who have produced these excellent results were inspired by this little book -- or by Fred Almgren himself.

The book is indeed a delightful invitation to the world of variational geometry. A central topic is Plateau's Problem, which is concerned with surfaces that model the behavior of soap films. When trying to resolve the problem, however, one soon finds that smooth surfaces are insufficient: Varifolds are needed. With varifolds, one can obtain geometrically meaningful solutions without having to know in advance all their possible singularities. This new tool makes possible much exciting new analysis and many new results.

Plateau's problem and varifolds live in the world of geometric measure theory, where differential geometry and measure theory combine to solve problems which have variational aspects. The author's hope in writing this book was to encourage young mathematicians to study this fascinating subject further. Judging from the success of his students, it achieves this exceedingly well.

Personal Details
Collection Status In Collection
Index 1485
Read It Yes
Links Barnes & Noble
Amazon Canada
Product Details
LoC Classification QA644 .A4 2001
Dewey 516.3/62
Edition Rev. ed.
Cover Price $20.07
No. of Pages 78
Originally published: New York : W.A. Benjamin, 1966, in series: Mathematics monograph series.