The curve shortening problem:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boca Raton, Fla. [u.a.]
Chapman & Hall/CRC
2001
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Includes bibliographical references (p. 247-253) and index |
| Physical Description: | IX, 255 S. |
| ISBN: | 1584882131 |
Staff View
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| 100 | 1 | |a Chou, Kai-Seng |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a The curve shortening problem |c Kai-Seng Chou ; Xi-Ping Zhu |
| 264 | 1 | |a Boca Raton, Fla. [u.a.] |b Chapman & Hall/CRC |c 2001 | |
| 300 | |a IX, 255 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
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| 650 | 4 | |a Curves on surfaces | |
| 650 | 4 | |a Flows (Differentiable dynamical systems) | |
| 650 | 4 | |a Hamiltonian systems | |
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Record in the Search Index
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|---|---|
| adam_text | V
CONTENTS
Preface vii
1 Basic Results 1
1.1 Short time existence 1
1.2 Facts from the parabolic theory 15
1.3 The evolution of geometric quantities 19
2 Invariant Solutions for the Curve Shortening Flow 27
2.1 Travelling waves 27
2.2 Spirals 29
2.3 The support function of a convex curve 33
2.4 Self similar solutions 35
3 The Curvature Eikonal Flow for Convex Curves 45
3.1 Blaschke Selection Theorem 45
3.2 Preserving convexity and shrinking to a point 47
3.3 Gage Hamilton Theorem 51
3.4 The contracting case of the ACEF 59
3.5 The stationary case of the ACEF 73
3.6 The expanding case of the ACEF 80
4 The Convex Generalized Curve Shortening Flow 93
4.1 Results from the Brunn Minkowski Theory 94
4.2 The AGCSF for a in (1/3, 1) 97
4.3 The affine curve shortening flow 102
4.4 Uniqueness of self similar solutions 112
5 The Non convex Curve Shortening Flow 121
5.1 An isoperimetric ratio 121
5.2 Limits of the rescaled flow 129
vi
5.3 Classification of singularities 134
6 A Class of Non convex Anisotropic Flows 143
6.1 The decrease in total absolute curvature 144
6.2 The existence of a limit curve 147
6.3 Shrinking to a point 153
6.4 A whisker lemma 160
6.5 The convexity theorem 164
7 Embedded Closed Geodesies on Surfaces 179
7.1 Basic results 180
7.2 The limit curve 186
7.3 Shrinking to a point 188
7.4 Convergence to a geodesic 196
8 The Non convex Generalized Curve Shortening
Flow 203
8.1 Short time existence 204
8.2 The number of convex arcs 211
8.3 The limit curve 218
8.4 Removal of interior singularities 228
8.5 The almost convexity theorem 239
Bibliography 247
Index 254
|
| any_adam_object | 1 |
| author | Chou, Kai-Seng Zhu, Xi-Ping |
| author_facet | Chou, Kai-Seng Zhu, Xi-Ping |
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| ctrlnum | (OCoLC)59525073 (DE-599)BVBBV013962552 |
| dewey-full | 516.352 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
| dewey-raw | 516.352 |
| dewey-search | 516.352 |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
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| id | DE-604.BV013962552 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:55:11Z |
| institution | BVB |
| isbn | 1584882131 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009555798 |
| oclc_num | 59525073 |
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| physical | IX, 255 S. |
| publishDate | 2001 |
| publishDateSearch | 2001 |
| publishDateSort | 2001 |
| publisher | Chapman & Hall/CRC |
| record_format | marc |
| spelling | Chou, Kai-Seng Verfasser aut The curve shortening problem Kai-Seng Chou ; Xi-Ping Zhu Boca Raton, Fla. [u.a.] Chapman & Hall/CRC 2001 IX, 255 S. txt rdacontent n rdamedia nc rdacarrier Includes bibliographical references (p. 247-253) and index Curves on surfaces Flows (Differentiable dynamical systems) Hamiltonian systems Hamiltonsches System (DE-588)4139943-2 gnd rswk-swf Differenzierbares dynamisches System (DE-588)4137931-7 gnd rswk-swf Fluss Mathematik (DE-588)4489499-5 gnd rswk-swf Kurve (DE-588)4033824-1 gnd rswk-swf Oberfläche (DE-588)4042907-6 gnd rswk-swf Hamiltonsches System (DE-588)4139943-2 s DE-604 Kurve (DE-588)4033824-1 s Oberfläche (DE-588)4042907-6 s Fluss Mathematik (DE-588)4489499-5 s Differenzierbares dynamisches System (DE-588)4137931-7 s Zhu, Xi-Ping Verfasser aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009555798&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Chou, Kai-Seng Zhu, Xi-Ping The curve shortening problem Curves on surfaces Flows (Differentiable dynamical systems) Hamiltonian systems Hamiltonsches System (DE-588)4139943-2 gnd Differenzierbares dynamisches System (DE-588)4137931-7 gnd Fluss Mathematik (DE-588)4489499-5 gnd Kurve (DE-588)4033824-1 gnd Oberfläche (DE-588)4042907-6 gnd |
| subject_GND | (DE-588)4139943-2 (DE-588)4137931-7 (DE-588)4489499-5 (DE-588)4033824-1 (DE-588)4042907-6 |
| title | The curve shortening problem |
| title_auth | The curve shortening problem |
| title_exact_search | The curve shortening problem |
| title_full | The curve shortening problem Kai-Seng Chou ; Xi-Ping Zhu |
| title_fullStr | The curve shortening problem Kai-Seng Chou ; Xi-Ping Zhu |
| title_full_unstemmed | The curve shortening problem Kai-Seng Chou ; Xi-Ping Zhu |
| title_short | The curve shortening problem |
| title_sort | the curve shortening problem |
| topic | Curves on surfaces Flows (Differentiable dynamical systems) Hamiltonian systems Hamiltonsches System (DE-588)4139943-2 gnd Differenzierbares dynamisches System (DE-588)4137931-7 gnd Fluss Mathematik (DE-588)4489499-5 gnd Kurve (DE-588)4033824-1 gnd Oberfläche (DE-588)4042907-6 gnd |
| topic_facet | Curves on surfaces Flows (Differentiable dynamical systems) Hamiltonian systems Hamiltonsches System Differenzierbares dynamisches System Fluss Mathematik Kurve Oberfläche |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009555798&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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