عنوان

Geometric measure theory :

(Number (ISBN

0080525601

(Number (ISBN

9780080525600

Erroneous ISBN

0125068514

Erroneous ISBN

9780125068512

Number

b720479

Title Proper

Geometric measure theory :

General Material Designation

[Book]

Other Title Information

a beginner's guide /

First Statement of Responsibility

Frank Morgan ; illustrated by James F. Bredt.

Edition Statement

3rd ed.

Place of Publication, Distribution, etc.

San Diego :

Name of Publisher, Distributor, etc.

Academic Press,

Date of Publication, Distribution, etc.

©2000.

Specific Material Designation and Extent of Item

1 online resource (ix, 226 pages) :

Other Physical Details

illustrations

Text of Note

Includes bibliographical references (pages 203-215) and indexes.

Text of Note

Preface. Geometric Measure Theory. Measures. Lipschitz Functions and Rectifiable Sets. Normal and Rectifiable Currents. The Compactness Theorem and the Existence of Area-Minimizing Surfaces. Examples of Area-Minimizing Surfaces. The Approximation Theorem. Survey of Regularity Results. Monotonicity and Oriented Tangent Cones. The Regularity of Area-Minimizing Hypersurfaces. Flat Chains Modulo v, Varifolds, and (M, E,)-Minimal Sets. Miscellaneous Useful Results. Soap Bubble Clusters. Proof of Double Bubble Conjecture. The Hexagonal Honeycomb and Kelvin Conjectures. Immiscible Fluids and Crystals. Isoperimetric Theorems in General Codimension. Solutions to Exercises. Bibliography. Index of Symbols. Name Index. Subject Index.

0

Text of Note

Geometric measure theory has become increasingly essential to geometry as well as numerous and varied physical applications. The third edition of this leading text/reference introduces the theory, the framework for the study of crystal growth, clusters of soap bubbles, and similar structures involving minimization of energy. Over the past thirty years, this theory has contributed to major advances in geometry and analysis including, for example, the original proof of the positive mass conjecture in cosmology. This third edition of Geometric Measure Theory: A Beginner's Guide presents, for the first time in print, the proofs of the double bubble and the hexagonal honeycomb conjectures. Four new chapters lead the reader through treatments of the Weaire-Phelan counterexample of Kelvin's conjecture, Almgren's optimal isoperimetric inequality, and immiscible fluids and crystals. The abundant illustrations, examples, exercises, and solutions in this book will enhance its reputation as the most accessible introduction to the subject.

Source for Acquisition/Subscription Address

Elsevier Science & Technology

Stock Number

89403:89403

Title

Geometric measure theory.

International Standard Book Number

9780125068512

Geometric measure theory.

Geometric measure theory.

MATHEMATICS-- Calculus.

MATHEMATICS-- Mathematical Analysis.

MAT-- 005000

MAT-- 034000

Number

Edition

Class number

Book number

Morgan, Frank, (Professor of Mathematics, Williams College)

Date of Transaction

20201208121411.0

Cataloguing Rules (Descriptive Conventions))

pn

Electronic name

[Book]

Y