Plateau's Problem

An Invitation to Varifold Geometry

Frederick J., Jr Almgren

76 pages, parution le 17/12/2001

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Résumé

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.

Contents

The phenomena of least area problems
Integration of differential forms over rectifiable sets
Varifolds
Variational problems involving varifolds
References
Index

Caractéristiques techniques

	PAPIER
Éditeur(s)	American Mathematical Society (AMS)
Auteur(s)	Frederick J., Jr Almgren
Parution	17/12/2001
Nb. de pages	76
Format	14 x 21,5
Couverture	Broché
Poids	100g
Intérieur	Noir et Blanc
EAN13	9780821827475
ISBN13	978-0-8218-2747-5