ENGLISH

Plateau's problem: an invitation to varifold geometry

By Frederick J Almgren

Book information

Publisher
W.A. Benjamin
Year
1966
ASIN
B0006BNSA2
Language
english
Format
DJVU
Filesize
2 MB (1663728 bytes)
Series
Mathematics monograph series
Edition
Benjamin
Pages
86\86
Library
Kolxo3
DPI
300
Scanned
yes
Time added
2009-07-20 03:45:11

Description

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.

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