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Geometric measure theorya beginner's...

Morgan, Frank.

Geometric measure theorya beginner's guide /

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Geometric measure theoryFrank Morgan ; illustrated by James F. Bredt.
其他題名:	a beginner's guide /
作者:	Morgan, Frank.
出版者:	San Diego :Academic Press,c2000.
面頁冊數:	ix, 226 p. :ill. ;24 cm.
標題:	Geometric measure theory.
電子資源:	An electronic book accessible through the World Wide Web; click for information
電子資源:	http://www.loc.gov/catdir/description/els031/00101595.html
電子資源:	http://www.loc.gov/catdir/toc/els031/00101595.html
ISBN:	9780125068512

Geometric measure theorya beginner's guide /
Morgan, Frank.

Geometric measure theorya beginner's guide /[electronic resource] :Frank Morgan ; illustrated by James F. Bredt. - 3rd ed. - San Diego :Academic Press,c2000. - ix, 226 p. :ill. ;24 cm.

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

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.

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.

Electronic reproduction.
Amsterdam :
Elsevier Science & Technology,
2007.

Mode of access: World Wide Web.

ISBN: 9780125068512

Source: 89403:89403Elsevier Science & Technologyhttp://www.sciencedirect.comSubjects--Topical Terms:

309750
Geometric measure theory.
Index Terms--Genre/Form:

214472
Electronic books.

LC Class. No.: QA312 / .M67 2000eb

Dewey Class. No.: 515/.42

Geometric measure theorya beginner's guide /
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020 $a 9780125068512
020 $a 0125068514
029 1 $a NZ1 $b 12432579
035 $a (OCoLC)162129409
035 $a ocn162129409
037 $a 89403:89403 $b Elsevier Science & Technology $n http://www.sciencedirect.com
040 $a OPELS $c OPELS
049 $a TEFA
050 1 4 $a QA312 $b .M67 2000eb
082 0 4 $a 515/.42 $2 22
100 1 $a Morgan, Frank. $3 189635
245 1 0 $a Geometric measure theory $h [electronic resource] : $b a beginner's guide / $c Frank Morgan ; illustrated by James F. Bredt.
250 $a 3rd ed.
260 $a San Diego : $b Academic Press, $c c2000.
300 $a ix, 226 p. : $b ill. ; $c 24 cm.
504 $a Includes bibliographical references (p. 203-215) and indexes.
505 0 $a 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.
520 $a 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.
533 $a Electronic reproduction. $b Amsterdam : $c Elsevier Science & Technology, $d 2007. $n Mode of access: World Wide Web. $n System requirements: Web browser. $n Title from title screen (viewed on July 25, 2007). $n Access may be restricted to users at subscribing institutions.
650 0 $a Geometric measure theory. $3 309750
655 7 $a Electronic books. $2 local. $3 214472
710 2 $a ScienceDirect (Online service) $3 307425
776 1 $c Original $z 0125068514 $z 9780125068512 $w (DLC) 00101595 $w (OCoLC)44995967
856 4 0 $3 ScienceDirect $u http://www.sciencedirect.com/science/book/9780125068512 $z An electronic book accessible through the World Wide Web; click for information
856 4 2 $3 Publisher description $u http://www.loc.gov/catdir/description/els031/00101595.html
856 4 1 $3 Table of contents $u http://www.loc.gov/catdir/toc/els031/00101595.html
994 $a C0 $b TEF

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http://www.loc.gov/catdir/description/els031/00101595.html
http://www.loc.gov/catdir/toc/els031/00101595.html

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