Some novel types of fractal geometry:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Oxford
Clarendon Press
2001
|
| Ausgabe: | 1. publ. |
| Schriftenreihe: | Oxford mathematical monographs
Oxford science publications |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | X, 164 S. |
| ISBN: | 0198508069 |
Internformat
MARC
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| 245 | 1 | 0 | |a Some novel types of fractal geometry |c Stephen Semmes |
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Datensatz im Suchindex
| _version_ | 1804128330232889344 |
|---|---|
| adam_text | CONTENTS
1 Introduction 1
1.1 Some aspects of calculus on Euclidean spaces 1
1.2 General metric spaces 3
1.3 The present monograph 8
1.4 Another perspective: curve families in metric spaces 8
2 Some background material 12
2.1 Doubling spaces 12
2.2 Ahlfors regular spaces 14
2.3 Poincare inequalities 15
2.4 Comparisons and examples 18
2.5 BPI spaces and BPI equivalence 34
3 A few basic topics 38
3.1 Only countably many? 38
3.2 A universal argument 42
3.3 Rectifiability 45
3.4 A slightly dumb case: dimensions 1 49
4 Deformations 51
4.1 Some general notions and examples 51
4.2 Doubling measures 53
4.3 Returning to general themes 63
4.4 Another view of the previous sections 66
5 Mappings between spaces 76
5.1 Questions, conjectures, and former conjectures 76
5.2 Regular mappings 80
5.3 Weak tangents 82
5.4 Finding regular behavior in Lipschitz mappings 85
5.5 Decent calculus and regular mappings 89
6 Some more general topics 93
6.1 A class of spaces, as from Laakso 93
6.2 Extremality 95
6.3 Looking at sets inside of spaces with decent calculus 99
6.4 Minimality and compression 103
6.5 Embeddings 109
7 A class of constructions to consider 112
7.1 The Heisenberg groups 112
x Contents
7.2 The Heisenberg fibrations 119
7.3 Questions about finding fibrations with interesting
structure 126
7.4 (s,i) Regular mappings 129
7.5 Some properties of (s, t) regular mappings 131
7.6 Special structure in particular situations 139
7.7 (s, t) Regular mappings and pushing geometry forward 141
8 Geometric structures and some topological configu¬
rations 144
Appendix
A Some side comments 149
A.I Differentiability and affine approximations 149
A.2 BPI spaces 151
A.3 Carnot spaces, and functions with values in a Carnot
group 151
References 154
Index 163
|
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| edition | 1. publ. |
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| id | DE-604.BV013535242 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:47:31Z |
| institution | BVB |
| isbn | 0198508069 |
| language | English |
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| physical | X, 164 S. |
| publishDate | 2001 |
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| series2 | Oxford mathematical monographs Oxford science publications |
| spelling | Semmes, Stephen Verfasser aut Some novel types of fractal geometry Stephen Semmes 1. publ. Oxford Clarendon Press 2001 X, 164 S. txt rdacontent n rdamedia nc rdacarrier Oxford mathematical monographs Oxford science publications Fractals Fraktalgeometrie (DE-588)4473576-5 gnd rswk-swf Fraktalgeometrie (DE-588)4473576-5 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009240077&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Semmes, Stephen Some novel types of fractal geometry Fractals Fraktalgeometrie (DE-588)4473576-5 gnd |
| subject_GND | (DE-588)4473576-5 |
| title | Some novel types of fractal geometry |
| title_auth | Some novel types of fractal geometry |
| title_exact_search | Some novel types of fractal geometry |
| title_full | Some novel types of fractal geometry Stephen Semmes |
| title_fullStr | Some novel types of fractal geometry Stephen Semmes |
| title_full_unstemmed | Some novel types of fractal geometry Stephen Semmes |
| title_short | Some novel types of fractal geometry |
| title_sort | some novel types of fractal geometry |
| topic | Fractals Fraktalgeometrie (DE-588)4473576-5 gnd |
| topic_facet | Fractals Fraktalgeometrie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009240077&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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