Geometric measure theory :: a beginner's guide /
Saved in:
| Main Author: | |
|---|---|
| Other Authors: | |
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Amsterdam :
Elsevier Ltd.,
2016.
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| Edition: | 5th edition. |
| Subjects: | |
| Online Access: | DE-862 DE-863 DE-862 DE-863 |
| Physical Description: | 1 online resource |
| ISBN: | 9780128045275 0128045272 |
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MARC
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| 245 | 1 | 0 | |a Geometric measure theory : |b a beginner's guide / |c Frank Morgan ; illustrated by James F. Bredt. |
| 250 | |a 5th edition. | ||
| 264 | 1 | |a Amsterdam : |b Elsevier Ltd., |c 2016. | |
| 300 | |a 1 online resource | ||
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| 505 | 0 | |a Front Cover ; Dedication ; Geometric Measure Theory: A Beginner's Guide ; Copyright ; Contents; Preface; Part I: Basic Theory; Chapter 1: Geometric Measure Theory ; 1.1 Archetypical Problem; 1.2 Surfaces as Mappings; 1.3 The Direct Method; 1.4 Rectifiable Currents; 1.5 The Compactness Theorem; 1.6 Advantages of Rectifiable Currents; 1.7 The Regularity of Area-Minimizing Rectifiable Currents ; 1.8 More General Ambient Spaces; Chapter 2: Measures ; 2.1 Definitions; 2.2 Lebesgue Measure; 2.3 Hausdorff Measure ; 2.4 Integral-Geometric Measure; 2.5 Densities ; 2.6 Approximate Limits. | |
| 505 | 8 | |a 2.7 Besicovitch Covering Theorem 2.8 Corollary; 2.9 Corollary; 2.10 Corollary; Exercises; Chapter 3: Lipschitz Functions and Rectifiable Sets ; 3.1 Lipschitz Functions; 3.2 Rademacher's Theorem ; 3.3 Approximation of a Lipschitz Function by a C1 Funcation ; 3.4 Lemma (Whitney's Extension Theorem) ; 3.5 Proposition ; 3.6 Jacobians; 3.7 The Area Formula ; 3.8 The Coarea Formula ; 3.9 Tangent Cones; 3.10 Rectifiable Sets ; 3.11 Proposition ; 3.12 Proposition ; 3.13 General Area-Coarea Formula ; 3.14 Product of Measures ; 3.15 Orientation; 3.16 Crofton's Formula ; 3.17 Structure Theorem. | |
| 505 | 8 | |a ExercisesChapter 4: Normal and Rectifiable Currents ; 4.1 Vectors and Differential Forms ; 4.2 Currents ; 4.3 Important Spaces of Currents ; 4.3A Mapping Currents; 4.3B Currents Representable by Integration; 4.4 Theorem ; 4.5 Normal Currents ; 4.6 Proposition ; 4.7 Theorem ; 4.8 Theorem ; 4.9 Constancy Theorem ; 4.10 Cartesian Products; 4.11 Slicing ; 4.12 Lemma ; 4.13 Proposition ; Exercises; Chapter 5: The Compactness Theorem and the Existence of Area-Minimizing Surfaces ; 5.1 The Deformation Theorem ; 5.2 Corollary; 5.3 The Isoperimetric Inequality ; 5.4 The Closure Theorem. | |
| 505 | 8 | |a 5.5 The Compactness Theorem 5.6 The Existence of Area-Minimizing Surfaces; 5.7 The Existence of Absolutely and Homologically Minimizing Surfaces in Manifolds ; Exercises; Chapter 6: Examples of Area-Minimizing Surfaces ; 6.1 The Minimal Surface Equation ; 6.2 Remarks on Higher Dimensions; 6.3 Complex Analytic Varieties ; 6.4 Fundamental Theorem of Calibrations; 6.5 History of Calibrations ; Exercises; Chapter 7: The Approximation Theorem ; 7.1 The Approximation Theorem ; Chapter 8: Survey of Regularity Results ; 8.1 Theorem ; 8.2 Theorem ; 8.3 Theorem ; 8.4 Boundary Regularity. | |
| 505 | 8 | |a 8.5 General Ambients, Volume Constraints, and Other IntegrandsExercises; Chapter 9: Monotonicity and Oriented Tangent Cones ; 9.1 Locally Integral Flat Chains ; 9.2 Monotonicity of the Mass Ratio; 9.3 Theorem ; 9.4 Corollary; 9.5 Corollary; 9.6 Corollary; 9.7 Oriented Tangent Cones ; 9.8 Theorem ; 9.9 Theorem; Exercises; Chapter 10: The Regularity of Area-Minimizing Hypersurfaces ; 10.1 Theorem; 10.2 Regularity for Area-Minimizing Hypersurfaces Theorem ; 10.3 Lemma ; 10.4 Maximum Principle; 10.5 Simons's Lemma ; 10.6 Lemma ; 10.7 Remarks; Exercises. | |
| 650 | 0 | |a Geometric measure theory. |0 http://id.loc.gov/authorities/subjects/sh85054124 | |
| 650 | 6 | |a Théorie de la mesure géométrique. | |
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| 650 | 7 | |a MATHEMATICS |x Mathematical Analysis. |2 bisacsh | |
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| author | Morgan, Frank (Professor of Mathematics, Williams College) |
| author2 | Bredt, James F. |
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| author_facet | Morgan, Frank (Professor of Mathematics, Williams College) Bredt, James F. |
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| author_sort | Morgan, Frank (Professor of Mathematics, Williams College) |
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| callnumber-raw | QA312 .M67 2016 |
| callnumber-search | QA312 .M67 2016 |
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| contents | Front Cover ; Dedication ; Geometric Measure Theory: A Beginner's Guide ; Copyright ; Contents; Preface; Part I: Basic Theory; Chapter 1: Geometric Measure Theory ; 1.1 Archetypical Problem; 1.2 Surfaces as Mappings; 1.3 The Direct Method; 1.4 Rectifiable Currents; 1.5 The Compactness Theorem; 1.6 Advantages of Rectifiable Currents; 1.7 The Regularity of Area-Minimizing Rectifiable Currents ; 1.8 More General Ambient Spaces; Chapter 2: Measures ; 2.1 Definitions; 2.2 Lebesgue Measure; 2.3 Hausdorff Measure ; 2.4 Integral-Geometric Measure; 2.5 Densities ; 2.6 Approximate Limits. 2.7 Besicovitch Covering Theorem 2.8 Corollary; 2.9 Corollary; 2.10 Corollary; Exercises; Chapter 3: Lipschitz Functions and Rectifiable Sets ; 3.1 Lipschitz Functions; 3.2 Rademacher's Theorem ; 3.3 Approximation of a Lipschitz Function by a C1 Funcation ; 3.4 Lemma (Whitney's Extension Theorem) ; 3.5 Proposition ; 3.6 Jacobians; 3.7 The Area Formula ; 3.8 The Coarea Formula ; 3.9 Tangent Cones; 3.10 Rectifiable Sets ; 3.11 Proposition ; 3.12 Proposition ; 3.13 General Area-Coarea Formula ; 3.14 Product of Measures ; 3.15 Orientation; 3.16 Crofton's Formula ; 3.17 Structure Theorem. ExercisesChapter 4: Normal and Rectifiable Currents ; 4.1 Vectors and Differential Forms ; 4.2 Currents ; 4.3 Important Spaces of Currents ; 4.3A Mapping Currents; 4.3B Currents Representable by Integration; 4.4 Theorem ; 4.5 Normal Currents ; 4.6 Proposition ; 4.7 Theorem ; 4.8 Theorem ; 4.9 Constancy Theorem ; 4.10 Cartesian Products; 4.11 Slicing ; 4.12 Lemma ; 4.13 Proposition ; Exercises; Chapter 5: The Compactness Theorem and the Existence of Area-Minimizing Surfaces ; 5.1 The Deformation Theorem ; 5.2 Corollary; 5.3 The Isoperimetric Inequality ; 5.4 The Closure Theorem. 5.5 The Compactness Theorem 5.6 The Existence of Area-Minimizing Surfaces; 5.7 The Existence of Absolutely and Homologically Minimizing Surfaces in Manifolds ; Exercises; Chapter 6: Examples of Area-Minimizing Surfaces ; 6.1 The Minimal Surface Equation ; 6.2 Remarks on Higher Dimensions; 6.3 Complex Analytic Varieties ; 6.4 Fundamental Theorem of Calibrations; 6.5 History of Calibrations ; Exercises; Chapter 7: The Approximation Theorem ; 7.1 The Approximation Theorem ; Chapter 8: Survey of Regularity Results ; 8.1 Theorem ; 8.2 Theorem ; 8.3 Theorem ; 8.4 Boundary Regularity. 8.5 General Ambients, Volume Constraints, and Other IntegrandsExercises; Chapter 9: Monotonicity and Oriented Tangent Cones ; 9.1 Locally Integral Flat Chains ; 9.2 Monotonicity of the Mass Ratio; 9.3 Theorem ; 9.4 Corollary; 9.5 Corollary; 9.6 Corollary; 9.7 Oriented Tangent Cones ; 9.8 Theorem ; 9.9 Theorem; Exercises; Chapter 10: The Regularity of Area-Minimizing Hypersurfaces ; 10.1 Theorem; 10.2 Regularity for Area-Minimizing Hypersurfaces Theorem ; 10.3 Lemma ; 10.4 Maximum Principle; 10.5 Simons's Lemma ; 10.6 Lemma ; 10.7 Remarks; Exercises. |
| ctrlnum | (OCoLC)948810773 |
| 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 | 5th edition. |
| format | Electronic eBook |
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| publishDate | 2016 |
| publishDateSearch | 2016 |
| publishDateSort | 2016 |
| publisher | Elsevier Ltd., |
| record_format | marc |
| spelling | Morgan, Frank (Professor of Mathematics, Williams College), author. https://id.oclc.org/worldcat/entity/E39PCjFJ6MmjwY8xpVVY6JFFXb http://id.loc.gov/authorities/names/no2016140969 Geometric measure theory : a beginner's guide / Frank Morgan ; illustrated by James F. Bredt. 5th edition. Amsterdam : Elsevier Ltd., 2016. 1 online resource text txt rdacontent computer c rdamedia online resource cr rdacarrier Online resource; title from PDF title page (EBSCO, viewed May 11, 2016). Front Cover ; Dedication ; Geometric Measure Theory: A Beginner's Guide ; Copyright ; Contents; Preface; Part I: Basic Theory; Chapter 1: Geometric Measure Theory ; 1.1 Archetypical Problem; 1.2 Surfaces as Mappings; 1.3 The Direct Method; 1.4 Rectifiable Currents; 1.5 The Compactness Theorem; 1.6 Advantages of Rectifiable Currents; 1.7 The Regularity of Area-Minimizing Rectifiable Currents ; 1.8 More General Ambient Spaces; Chapter 2: Measures ; 2.1 Definitions; 2.2 Lebesgue Measure; 2.3 Hausdorff Measure ; 2.4 Integral-Geometric Measure; 2.5 Densities ; 2.6 Approximate Limits. 2.7 Besicovitch Covering Theorem 2.8 Corollary; 2.9 Corollary; 2.10 Corollary; Exercises; Chapter 3: Lipschitz Functions and Rectifiable Sets ; 3.1 Lipschitz Functions; 3.2 Rademacher's Theorem ; 3.3 Approximation of a Lipschitz Function by a C1 Funcation ; 3.4 Lemma (Whitney's Extension Theorem) ; 3.5 Proposition ; 3.6 Jacobians; 3.7 The Area Formula ; 3.8 The Coarea Formula ; 3.9 Tangent Cones; 3.10 Rectifiable Sets ; 3.11 Proposition ; 3.12 Proposition ; 3.13 General Area-Coarea Formula ; 3.14 Product of Measures ; 3.15 Orientation; 3.16 Crofton's Formula ; 3.17 Structure Theorem. ExercisesChapter 4: Normal and Rectifiable Currents ; 4.1 Vectors and Differential Forms ; 4.2 Currents ; 4.3 Important Spaces of Currents ; 4.3A Mapping Currents; 4.3B Currents Representable by Integration; 4.4 Theorem ; 4.5 Normal Currents ; 4.6 Proposition ; 4.7 Theorem ; 4.8 Theorem ; 4.9 Constancy Theorem ; 4.10 Cartesian Products; 4.11 Slicing ; 4.12 Lemma ; 4.13 Proposition ; Exercises; Chapter 5: The Compactness Theorem and the Existence of Area-Minimizing Surfaces ; 5.1 The Deformation Theorem ; 5.2 Corollary; 5.3 The Isoperimetric Inequality ; 5.4 The Closure Theorem. 5.5 The Compactness Theorem 5.6 The Existence of Area-Minimizing Surfaces; 5.7 The Existence of Absolutely and Homologically Minimizing Surfaces in Manifolds ; Exercises; Chapter 6: Examples of Area-Minimizing Surfaces ; 6.1 The Minimal Surface Equation ; 6.2 Remarks on Higher Dimensions; 6.3 Complex Analytic Varieties ; 6.4 Fundamental Theorem of Calibrations; 6.5 History of Calibrations ; Exercises; Chapter 7: The Approximation Theorem ; 7.1 The Approximation Theorem ; Chapter 8: Survey of Regularity Results ; 8.1 Theorem ; 8.2 Theorem ; 8.3 Theorem ; 8.4 Boundary Regularity. 8.5 General Ambients, Volume Constraints, and Other IntegrandsExercises; Chapter 9: Monotonicity and Oriented Tangent Cones ; 9.1 Locally Integral Flat Chains ; 9.2 Monotonicity of the Mass Ratio; 9.3 Theorem ; 9.4 Corollary; 9.5 Corollary; 9.6 Corollary; 9.7 Oriented Tangent Cones ; 9.8 Theorem ; 9.9 Theorem; Exercises; Chapter 10: The Regularity of Area-Minimizing Hypersurfaces ; 10.1 Theorem; 10.2 Regularity for Area-Minimizing Hypersurfaces Theorem ; 10.3 Lemma ; 10.4 Maximum Principle; 10.5 Simons's Lemma ; 10.6 Lemma ; 10.7 Remarks; Exercises. Geometric measure theory. http://id.loc.gov/authorities/subjects/sh85054124 Théorie de la mesure géométrique. MATHEMATICS Calculus. bisacsh MATHEMATICS Mathematical Analysis. bisacsh Geometric measure theory fast Electronic book. Bredt, James F., illustrator. has work: Geometric measure theory (Text) https://id.oclc.org/worldcat/entity/E39PCG633bqwgqMDbvM4MM68vd https://id.oclc.org/worldcat/ontology/hasWork Print version : 9780128044896 |
| spellingShingle | Morgan, Frank (Professor of Mathematics, Williams College) Geometric measure theory : a beginner's guide / Front Cover ; Dedication ; Geometric Measure Theory: A Beginner's Guide ; Copyright ; Contents; Preface; Part I: Basic Theory; Chapter 1: Geometric Measure Theory ; 1.1 Archetypical Problem; 1.2 Surfaces as Mappings; 1.3 The Direct Method; 1.4 Rectifiable Currents; 1.5 The Compactness Theorem; 1.6 Advantages of Rectifiable Currents; 1.7 The Regularity of Area-Minimizing Rectifiable Currents ; 1.8 More General Ambient Spaces; Chapter 2: Measures ; 2.1 Definitions; 2.2 Lebesgue Measure; 2.3 Hausdorff Measure ; 2.4 Integral-Geometric Measure; 2.5 Densities ; 2.6 Approximate Limits. 2.7 Besicovitch Covering Theorem 2.8 Corollary; 2.9 Corollary; 2.10 Corollary; Exercises; Chapter 3: Lipschitz Functions and Rectifiable Sets ; 3.1 Lipschitz Functions; 3.2 Rademacher's Theorem ; 3.3 Approximation of a Lipschitz Function by a C1 Funcation ; 3.4 Lemma (Whitney's Extension Theorem) ; 3.5 Proposition ; 3.6 Jacobians; 3.7 The Area Formula ; 3.8 The Coarea Formula ; 3.9 Tangent Cones; 3.10 Rectifiable Sets ; 3.11 Proposition ; 3.12 Proposition ; 3.13 General Area-Coarea Formula ; 3.14 Product of Measures ; 3.15 Orientation; 3.16 Crofton's Formula ; 3.17 Structure Theorem. ExercisesChapter 4: Normal and Rectifiable Currents ; 4.1 Vectors and Differential Forms ; 4.2 Currents ; 4.3 Important Spaces of Currents ; 4.3A Mapping Currents; 4.3B Currents Representable by Integration; 4.4 Theorem ; 4.5 Normal Currents ; 4.6 Proposition ; 4.7 Theorem ; 4.8 Theorem ; 4.9 Constancy Theorem ; 4.10 Cartesian Products; 4.11 Slicing ; 4.12 Lemma ; 4.13 Proposition ; Exercises; Chapter 5: The Compactness Theorem and the Existence of Area-Minimizing Surfaces ; 5.1 The Deformation Theorem ; 5.2 Corollary; 5.3 The Isoperimetric Inequality ; 5.4 The Closure Theorem. 5.5 The Compactness Theorem 5.6 The Existence of Area-Minimizing Surfaces; 5.7 The Existence of Absolutely and Homologically Minimizing Surfaces in Manifolds ; Exercises; Chapter 6: Examples of Area-Minimizing Surfaces ; 6.1 The Minimal Surface Equation ; 6.2 Remarks on Higher Dimensions; 6.3 Complex Analytic Varieties ; 6.4 Fundamental Theorem of Calibrations; 6.5 History of Calibrations ; Exercises; Chapter 7: The Approximation Theorem ; 7.1 The Approximation Theorem ; Chapter 8: Survey of Regularity Results ; 8.1 Theorem ; 8.2 Theorem ; 8.3 Theorem ; 8.4 Boundary Regularity. 8.5 General Ambients, Volume Constraints, and Other IntegrandsExercises; Chapter 9: Monotonicity and Oriented Tangent Cones ; 9.1 Locally Integral Flat Chains ; 9.2 Monotonicity of the Mass Ratio; 9.3 Theorem ; 9.4 Corollary; 9.5 Corollary; 9.6 Corollary; 9.7 Oriented Tangent Cones ; 9.8 Theorem ; 9.9 Theorem; Exercises; Chapter 10: The Regularity of Area-Minimizing Hypersurfaces ; 10.1 Theorem; 10.2 Regularity for Area-Minimizing Hypersurfaces Theorem ; 10.3 Lemma ; 10.4 Maximum Principle; 10.5 Simons's Lemma ; 10.6 Lemma ; 10.7 Remarks; Exercises. Geometric measure theory. http://id.loc.gov/authorities/subjects/sh85054124 Théorie de la mesure géométrique. MATHEMATICS Calculus. bisacsh MATHEMATICS Mathematical Analysis. bisacsh Geometric measure theory fast |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85054124 |
| 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 | Geometric measure theory. http://id.loc.gov/authorities/subjects/sh85054124 Théorie de la mesure géométrique. MATHEMATICS Calculus. bisacsh MATHEMATICS Mathematical Analysis. bisacsh Geometric measure theory fast |
| topic_facet | Geometric measure theory. Théorie de la mesure géométrique. MATHEMATICS Calculus. MATHEMATICS Mathematical Analysis. Geometric measure theory Electronic book. |
| work_keys_str_mv | AT morganfrank geometricmeasuretheoryabeginnersguide AT bredtjamesf geometricmeasuretheoryabeginnersguide |