Rectifiable sets, densities and tangent measures:
Gespeichert in:
| Beteilige Person: | |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Zürich
European Math. Soc.
2008
|
| Schriftenreihe: | Zurich lectures in advanced mathematics
|
| Schlagwörter: | |
| Links: | http://deposit.dnb.de/cgi-bin/dokserv?id=3063112&prov=M&dok_var=1&dok_ext=htm http://www.ems-ph.org/book.php?proj_nr=67 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 |
| Umfang: | VI, 124 S. |
| ISBN: | 9783037190449 3037190442 |
Internformat
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Datensatz im Suchindex
| _version_ | 1819380535281057792 |
|---|---|
| adam_text | 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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| id | DE-604.BV035227968 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-20T13:26:22Z |
| institution | BVB |
| isbn | 9783037190449 3037190442 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-017033969 |
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| physical | VI, 124 S. |
| publishDate | 2008 |
| publishDateSearch | 2008 |
| publishDateSort | 2008 |
| publisher | European Math. Soc. |
| record_format | marc |
| series2 | Zurich lectures in advanced mathematics |
| 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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