Ricci flow and the sphere theorem:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Providence, Rhode Island
American Mathematical Society
[2010]
|
| Schriftenreihe: | Graduate studies in mathematics
volume 111 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | vii, 176 Seiten |
| ISBN: | 9780821849385 |
Internformat
MARC
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| 245 | 1 | 0 | |a Ricci flow and the sphere theorem |c Simon Brendle |
| 264 | 1 | |a Providence, Rhode Island |b American Mathematical Society |c [2010] | |
| 264 | 4 | |c © 2010 | |
| 300 | |a vii, 176 Seiten | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Graduate studies in mathematics |v volume 111 | |
| 650 | 4 | |a Ricci flow | |
| 650 | 4 | |a Sphere | |
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Datensatz im Suchindex
| _version_ | 1804140994387509248 |
|---|---|
| adam_text | Contents
Preface
v
Chapter
1.
A survey of sphere theorems in geometry
1
§1.1.
Riemannian geometry background
1
§1.2.
The Topological Sphere Theorem
6
§1.3.
The Diameter Sphere Theorem
7
§1.4.
The Sphere Theorem of Micallef and Moore
9
§1.5.
Exotic Spheres and the
Diíferentiable
Sphere Theorem
13
Chapter
2.
Hamilton s
Ricci
flow
15
§2.1.
Definition and special solutions
15
§2.2.
Short-time existence and uniqueness
17
§2.3.
Evolution of the Riemann curvature tensor
21
§2.4.
Evolution of the
Ricci
and scalar curvature
28
Chapter
3.
Interior estimates
31
§3.1.
Estimates for the derivatives of the curvature tensor
31
§3.2.
Derivative estimates for tensors
33
§3.3.
Curvature blow-up at finite-time singularities
36
Chapter
4.
Ricci
flow on S2
37
§4.1.
Gradient
Ricci solitone
on
S2
37
§4.2.
Monotonicity
of Hamilton s entropy functional
39
§4.3.
Convergence to a constant curvature metric
45
Chapter
5.
Pointwise curvature estimates
49
§5.1.
Introduction
49
iii
iv Contents
§5.2.
The tangent and normal cone to a convex set
49
§5.3.
Hamilton s maximum principle for the
Ricci
flow
53
§5.4.
Hamilton s convergence criterion for the
Ricci
now
58
Chapter
6.
Curvature pinching in dimension
3 67
§6.1.
Three-manifolds with positive
Ricci
curvature
67
§6.2.
The curvature estimate of Hamilton and Ivey
70
Chapter
7.
Preserved curvature conditions in higher dimensions
73
§7.1.
Introduction
73
§7.2.
Nonnegative isotropie
curvature
74
§7.3.
Proof of Proposition
7.4 77
§7.4.
The cone
Õ
87
§7.5.
The cone
С
90
§7.6.
An invariant set which lies between
Č
and
Ô
93
§7.7.
An overview of various curvature conditions
100
Chapter
8.
Convergence results in higher dimensions
101
§8.1.
An algebraic identity for curvature tensors
101
§8.2.
Constructing a family of invariant cones
106
§8.3.
Proof of the Differentiable Sphere Theorem
112
§8.4.
An improved convergence theorem
117
Chapter
9.
Rigidity results
121
§9.1.
Introduction
121
§9.2.
Berger s classification of holonomy groups
121
§9.3.
A version of the strict maximum principle
123
§9.4.
Three-manifolds with
nonnegative Ricci
curvature
126
§9.5.
Manifolds with
nonnegative isotropie
curvature
129
§9.6.
Kähler-Einstein
and
quaternionic-Kähler
manifolds
135
§9.7.
A generalization of a theorem of Tachibana
146
§9.8.
Classification results
149
Appendix A. Convergence of evolving metrics
155
Appendix B. Results from complex linear algebra
159
Problems
Bibliography
Index 175
|
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| discipline | Mathematik |
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| id | DE-604.BV035971426 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T22:08:49Z |
| institution | BVB |
| isbn | 9780821849385 |
| language | English |
| lccn | 2009037261 |
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| physical | vii, 176 Seiten |
| publishDate | 2010 |
| publishDateSearch | 2010 |
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| publisher | American Mathematical Society |
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| series | Graduate studies in mathematics |
| series2 | Graduate studies in mathematics |
| spelling | Brendle, Simon 1981- Verfasser (DE-588)123040310 aut Ricci flow and the sphere theorem Simon Brendle Providence, Rhode Island American Mathematical Society [2010] © 2010 vii, 176 Seiten txt rdacontent n rdamedia nc rdacarrier Graduate studies in mathematics volume 111 Ricci flow Sphere Ricci-Fluss (DE-588)7531847-7 gnd rswk-swf Ricci-Fluss (DE-588)7531847-7 s DE-604 Erscheint auch als Online-Ausgabe 978-1-4704-1173-2 Graduate studies in mathematics volume 111 (DE-604)BV009739289 111 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018865429&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Brendle, Simon 1981- Ricci flow and the sphere theorem Graduate studies in mathematics Ricci flow Sphere Ricci-Fluss (DE-588)7531847-7 gnd |
| subject_GND | (DE-588)7531847-7 |
| title | Ricci flow and the sphere theorem |
| title_auth | Ricci flow and the sphere theorem |
| title_exact_search | Ricci flow and the sphere theorem |
| title_full | Ricci flow and the sphere theorem Simon Brendle |
| title_fullStr | Ricci flow and the sphere theorem Simon Brendle |
| title_full_unstemmed | Ricci flow and the sphere theorem Simon Brendle |
| title_short | Ricci flow and the sphere theorem |
| title_sort | ricci flow and the sphere theorem |
| topic | Ricci flow Sphere Ricci-Fluss (DE-588)7531847-7 gnd |
| topic_facet | Ricci flow Sphere Ricci-Fluss |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018865429&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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