Rectifiable sets, densities and tangent measures:
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Zürich
European Math. Soc.
2008
|
| Series: | Zurich lectures in advanced mathematics
|
| Subjects: | |
| Online Access: | Inhaltstext Ausfuehrliche Beschreibung Inhaltsverzeichnis |
| Physical Description: | VI, 124 S. |
| ISBN: | 9783037190449 3037190442 |
Staff View
MARC
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| 245 | 1 | 0 | |a Rectifiable sets, densities and tangent measures |c Camillo de Lellis |
| 264 | 1 | |a Zürich |b European Math. Soc. |c 2008 | |
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Record in the Search Index
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Contents
1 Introduction 1
2 Notation and preliminaries 4
2.1 General notation and measures 4
2.2 Weak* convergence of measures 5
2.3 Covering theorems and differentiation of measures 9
2.4 Hausdorff measures 10
2.5 Lipschitz functions 11
2.6 The Stone-Weierstrass Theorem 12
3 Marstrand's Theorem and tangent measures 13
3.1 Tangent measures and Proposition 3.4 16
3.2 Lemma 3.7 and some easy remarks 21
3.3 Proof of Lemma 3.8 22
3.4 Proof of Corollary 3.9 25
4 Rectifiability 27
4.1 The Area Formula I: Preliminary lemmas 29
4.2 The Area Formula II 32
4.3 The Geometric Lemma and the Rectifiability Criterion 35
4.4 Proof of Theorem 4.8 37
5 The Marstrand-Mattila Rectifiability Criterion 40
5.1 Preliminaries: Purely unrectifiable sets and projections 42
5.2 The proof of the Marstrand-Mattila rectifiability criterion 47
5.3 Proof of Theorem 5.1 53
6 An overview of Preiss' proof 56
6.1 The cone {xj - x\ + x\ + xj}, 59
6.2 Part A of Preiss' strategy 63
6.3 Part B of Preiss' strategy: Three main steps 65
6.4 From the three main steps to the proof of Theorem 6.10 66
7 Moments and uniqueness of the tangent measure at infinity 70
7.1 From Proposition 7.7 to the uniqueness of the tangent measure at
infinity 74
7.2 Elementary bounds on bk,s and the expansion (7.5) 76
7.3 Proof of Proposition 7.7 79
vi Contents
8 Flat versus curved at infinity 85
8.1 The tangent measure at infinity is a cone 88
8.2 Conical uniform measures 88
8.3 Proof of Proposition 8.5 91
9 Flatness at infinity implies flatness 95
9.1 Proofs of (ii) and (iv) 99
9.2 An integral formula for tr(42)LF) 100
9.3 An intermediate inequality 103
9.4 Proof of (9.7) and conclusion 106
10 Open problems 110
AppendixA. Proof of Theorem 3.11 117
Appendix B. Gaussian integrals 122
Bibliography 125
Index 127 |
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| spelling | De Lellis, Camillo 1976- Verfasser (DE-588)122562321 aut Rectifiable sets, densities and tangent measures Camillo de Lellis Zürich European Math. Soc. 2008 VI, 124 S. txt rdacontent n rdamedia nc rdacarrier Zurich lectures in advanced mathematics Geometric measure theory Geometrische Maßtheorie (DE-588)4125258-5 gnd rswk-swf Geometrische Maßtheorie (DE-588)4125258-5 s DE-604 text/html http://deposit.dnb.de/cgi-bin/dokserv?id=3063112&prov=M&dok_var=1&dok_ext=htm Inhaltstext text/html http://www.ems-ph.org/book.php?proj_nr=67 Ausfuehrliche Beschreibung HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017033969&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | De Lellis, Camillo 1976- Rectifiable sets, densities and tangent measures Geometric measure theory Geometrische Maßtheorie (DE-588)4125258-5 gnd |
| subject_GND | (DE-588)4125258-5 |
| title | Rectifiable sets, densities and tangent measures |
| title_auth | Rectifiable sets, densities and tangent measures |
| title_exact_search | Rectifiable sets, densities and tangent measures |
| title_full | Rectifiable sets, densities and tangent measures Camillo de Lellis |
| title_fullStr | Rectifiable sets, densities and tangent measures Camillo de Lellis |
| title_full_unstemmed | Rectifiable sets, densities and tangent measures Camillo de Lellis |
| title_short | Rectifiable sets, densities and tangent measures |
| title_sort | rectifiable sets densities and tangent measures |
| topic | Geometric measure theory Geometrische Maßtheorie (DE-588)4125258-5 gnd |
| topic_facet | Geometric measure theory Geometrische Maßtheorie |
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