Plateau's Problem : An Invitation to Varifold Geometry

By: Frederick J. Almgren

Write A Review

Paperback

At a Glance

Paperback
88 Pages

Dimensions(cm)
22.23 x 14.61 x 0.64

Paperback

$136.25

or 4 interest-free payments of $34.06 with

or

Aims to ship in 15 to 25 business days

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 newanalysis 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.

Shipping

	Standard Shipping	Express Shipping
Metro postcodes:	$9.99	$14.95
Regional postcodes:	$9.99	$14.95
Rural postcodes:	$9.99	$14.95

How to return your order

At Booktopia, we offer hassle-free returns in accordance with our returns policy. If you wish to return an item, please get in touch with Booktopia Customer Care.

Additional postage charges may be applicable.

Defective items

If there is a problem with any of the items received for your order then the Booktopia Customer Care team is ready to assist you.

For more info please visit our Help Centre.

More in Geometry

Calculus

3rd Edition

Hardcover

RRP $91.95

$79.90

13%
OFF

The Maths Book

Big Ideas Simply Explained

Hardcover

RRP $42.99

$32.75

24%
OFF

The Golden Ratio

Divine Beauty of Mathematics

Hardcover

RRP $55.00

$46.35

16%
OFF

Sum Stories Equations and Their Origins : Equations and Their Origins - Robin Wilson

$265.95

23%
OFF

The Inductive Blockwise Alperin Weight Condition for the Chevalley Group_4(q)$

Paperback

RRP $219.00

$168.80

23%
OFF

Geometry, Groups and Mathematical Philosophy

Paperback

RRP $347.00

$265.95

23%
OFF

$p$-Adic Hodge Theory for Artin Stacks

Paperback

RRP $219.00

$168.80

23%
OFF

Drinfeld Modular Forms of Arbitrary Rank

Paperback

RRP $219.00

$168.80

23%
OFF

Lectures on Differential Geometry

Paperback

RRP $229.00

$175.75

23%
OFF

Introduction to Lie Algebras

Finite and Infinite Dimension

Hardcover

RRP $347.00

$265.95

23%
OFF

Introduction to Lie Algebras

Finite and Infinite Dimension

Paperback

RRP $229.00

$175.75

23%
OFF

The Practice of Algebraic Curves

A Second Course in Algebraic Geometry

Paperback

RRP $229.00

$175.75

23%
OFF

Bimonoidal Categories, $E_n$-Monoidal Categories, and Algebraic $K$-Theory : Volume III: From Categories to Structured Ring Spectra - Niles Johnson

$35.25

12%
OFF

Regents Exams and Answers

Geometry, Sixth Edition

Paperback

RRP $39.99

$35.25

12%
OFF

Convex Functions and Their Applications

A Contemporary Approach

Hardcover

$246.35

Foreword to the AMS Edition	p. ix
Editors' Foreword	p. xiii
Preface	p. xv
The Phenomena of Least Area Problems	p. 1
Integration of Differential Forms over Rectifiable Sets	p. 15
Notation	p. 15
Hausdorff measure	p. 16
The Grassmann algebra and its dual	p. 19
Differential forms	p. 22
The Grassmann manifolds associated with R[superscript 3]	p. 23
Integration of differential forms over manifolds	p. 25
Rectifiable sets	p. 31
Integration of differential forms over rectifiable sets	p. 35
Varifolds	p. 37
Rectifiable sets regarded as real valued functions on the space of differential forms	p. 37
Rectifiable geometry, current geometry, and varifold geometry	p. 39
Varifolds	p. 44
The weight of a varifold	p. 48
Elementary varifolds	p. 52
Mappings of varifolds	p. 53
Variational Problems Involving Varifolds	p. 55
Vector fields and deformations	p. 55
Variations	p. 56
Boundaries	p. 58
Curvature and mean curvature	p. 62
The compactness theorem for regular integral varifolds	p. 67
A solution to the existence portion of Plateau's problem	p. 69
Useful facts about varifolds	p. 71
References	p. 73
Additional References	p. 75
Index	p. 77
Table of Contents provided by Syndetics. All Rights Reserved.

Plateau's Problem : An Invitation to Varifold Geometry

At a Glance

Paperback

Shipping

How to return your order

Defective items

You Can Find This Book In

More in Geometry

Calculus

3rd Edition

The Maths Book

Big Ideas Simply Explained

The Golden Ratio

Divine Beauty of Mathematics

Sum Stories Equations and Their Origins

Equations and Their Origins

Topology at Infinity of Discrete Groups

The Inductive Blockwise Alperin Weight Condition for the Chevalley Group_4(q)$

Geometry, Groups and Mathematical Philosophy

$p$-Adic Hodge Theory for Artin Stacks