Geometric measure theory: a beginner's guide
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
San Diego
Academic Press
c2000
|
| Ausgabe: | 3rd ed |
| Schlagworte: | |
| Online-Zugang: | FAW01 FAW02 Volltext |
| Beschreibung: | 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 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 Includes bibliographical references (p. 203-215) and indexes |
| Beschreibung: | 1 Online-Ressource (ix, 226 p.) |
| ISBN: | 0080525601 0125068514 9780080525600 9780125068512 |
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| 500 | |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 | ||
| 500 | |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 | ||
| 500 | |a Includes bibliographical references (p. 203-215) and indexes | ||
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Datensatz im Suchindex
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| author | Morgan, Frank |
| author_facet | Morgan, Frank |
| author_role | aut |
| author_sort | Morgan, Frank |
| author_variant | f m fm |
| building | Verbundindex |
| bvnumber | BV043044593 |
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| dewey-full | 515/.42 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515/.42 |
| dewey-search | 515/.42 |
| dewey-sort | 3515 242 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 3rd ed |
| format | Electronic eBook |
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| isbn | 0080525601 0125068514 9780080525600 9780125068512 |
| language | English |
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| spelling | Morgan, Frank Verfasser aut Geometric measure theory a beginner's guide Frank Morgan ; illustrated by James F. Bredt 3rd ed San Diego Academic Press c2000 1 Online-Ressource (ix, 226 p.) txt rdacontent c rdamedia cr rdacarrier 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 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 Includes bibliographical references (p. 203-215) and indexes MATHEMATICS / Calculus bisacsh MATHEMATICS / Mathematical Analysis bisacsh Geometric measure theory fast Geometric measure theory Geometrische Maßtheorie (DE-588)4125258-5 gnd rswk-swf Geometrische Maßtheorie (DE-588)4125258-5 s 1\p DE-604 http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=198954 Aggregator Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Morgan, Frank Geometric measure theory a beginner's guide MATHEMATICS / Calculus bisacsh MATHEMATICS / Mathematical Analysis bisacsh Geometric measure theory fast Geometric measure theory Geometrische Maßtheorie (DE-588)4125258-5 gnd |
| subject_GND | (DE-588)4125258-5 |
| title | Geometric measure theory a beginner's guide |
| title_auth | Geometric measure theory a beginner's guide |
| title_exact_search | Geometric measure theory a beginner's guide |
| title_full | Geometric measure theory a beginner's guide Frank Morgan ; illustrated by James F. Bredt |
| title_fullStr | Geometric measure theory a beginner's guide Frank Morgan ; illustrated by James F. Bredt |
| title_full_unstemmed | Geometric measure theory a beginner's guide Frank Morgan ; illustrated by James F. Bredt |
| title_short | Geometric measure theory |
| title_sort | geometric measure theory a beginner s guide |
| title_sub | a beginner's guide |
| topic | MATHEMATICS / Calculus bisacsh MATHEMATICS / Mathematical Analysis bisacsh Geometric measure theory fast Geometric measure theory Geometrische Maßtheorie (DE-588)4125258-5 gnd |
| topic_facet | MATHEMATICS / Calculus MATHEMATICS / Mathematical Analysis Geometric measure theory Geometrische Maßtheorie |
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