The Ricci Flow: techniques and applications: IV Long-time solutions and related topics
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| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, Rhode Island
American Mathematical Society
[2015]
|
| Series: | Mathematical surveys and monographs
volume 206 |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | xx, 374 Seiten Diagramme |
| ISBN: | 9780821849910 |
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| 264 | 1 | |a Providence, Rhode Island |b American Mathematical Society |c [2015] | |
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Record in the Search Index
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Contents
Preface ix
Acknowledgments xiii
Contents of Volume One and Parts I, II, and III of Volume Two xv
Notation and Symbols xvii
Chapter 27. Noncompact Gradient Ricci Solitons I
1. Basic properties of gradient Ricci solitons 1
2. Estimates for potential functions of gradient solitons 9
3. Lower bounds for the scalar curvature of nonflat nonexpanding
gradient Ricci solitons 15
4. Volume growth of shrinking gradient Ricci solitons 17
5. Logarithmic Sobolev inequality 26
6. Gradient shrinkers with nonnegative Ricci curvature 29
7. Notes and commentary 33
Chapter 28. Special Ancient Solutions 35
1. Local estimate for the scalar curvature under Ricci flow 35
2. Properties of singularity models 40
3. Noncompact 2-diinensional ancient solutions with finite width 49
4. Ancient solutions with positive curvature 63
5. Notes and commentary 66
Chapter 29. Compact 2-Dimensional Ancient Solutions 69
1. Statement of the classification result and outline of its proof 69
2. The Ricci flow equation on S2 and some intuition 70
3. The King-Rosenau solution in the various coordinates 73
4. A priori estimates for the pressure function 76
5. The almost everywhere vanishing of 79
6. First properties of the backward limit 81
7. Isoperimetric constant of metrics on S2 83
8. Characterizing round solutions 87
9. Classifying the backward pointwise limit 100
10. An unrescaled cigar backward Cheeger-Gromov limit 106
11. Irreducible components of V3e 108
12. The heat-type equation satisfied by Q 111
13. That Q = 0 implies the solution is the King-Rosenau solution 117
14. The evolution equation for Q 124
15. The quantity Q must be identically zero 125
V
CONTENTS
16. The equivalence of Q and Q 129
17. Notes and commentary 132
Chapter 30. Type I Singularities and Ancient Solutions 133
1. Reduced distance of Type A solutions 133
2. Reduced volume at the singular time for Type I solutions 145
3. Type I solutions have shrinker singularity models 154
4. Some results on Type I ancient solutions 159
5. Notes and commentary 169
Chapter 31. Hyperbolic Geometry and 3-Manifolds 171
1. Introduction to hyperbolic space 171
2. Topology and geometry of hyperbolic 3-manifolds 178
3. The Margulis lemma and hyperbolic cusps 185
4. Mostow rigidity 192
5. Seifert fibered manifolds and graph manifolds 193
6. Notes and commentary 194
Chapter 32. Nonsingular Solutions on Closed 3-Manifolds 197
1. Introduction 197
2. The main result on nonsingular solutions 200
3. The three cases of nonsingular solutions 203
4. The positive and zero cases of nonsingular solutions 207
5. The negative case—sequential limits must be hyperbolic 210
6. Notes and commentary 211
Chapter 33. Noncompact Hyperbolic Limits 213
1. Main results on hyperbolic pieces 214
2. Harmonic maps parametrizing almost hyperbolic pieces 219
3. Proof of the stability of hyperbolic limits 226
4. Incompressibility of boundary tori of hyperbolic pieces 237
5. Notes and commentary 254
Chapter 34. Constant Mean Curvature Surfaces and Harmonic Maps
by IFT 257
1. Constant mean curvature surfaces 257
2. Harmonic maps near the identity of Sn 260
3. Existence of harmonic maps near the identity of manifolds with
negative Ricci curvature 266
4. Application of Mostow rigidity to the existence of isometries 273
5. Notes and commentary 278
Chapter 35. Stability of Ricci Flow 279
1. Linear stability of Ricci flow 280
2. Analytic semigroups and maximal regularity theory 287
3. Dynamic stability results obtained using linearization 296
4. Dynamic stability results obtained by other methods 304
CONTENTS vii
Chapter 36. Type II Singularities and Degenerate Neckpinches 307
1. Numerical simulation of solutions with degenerate neckpinches 309
2. Matched asymptotic studies of degenerate neckpinches 318
3. Ricci flow solutions with degenerate neckpinch singularities 324
4. Concluding remarks 326
Appendix K. Implicit Function Theorem 327
1. The implicit function theorem 327
2. Holder spaces and Sobolev spaces on manifolds 332
3. Harmonic maps and their linearization 336
4. Spectrum of Aj on p-forms on Sn 347
5. Notes and commentary 352
Bibliography 353
Index 371 |
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| physical | xx, 374 Seiten Diagramme |
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| spelling | Chow, Bennett 1962- Verfasser (DE-588)136099793 aut The Ricci Flow: techniques and applications IV Long-time solutions and related topics Bennett Chow, Sun-Chin Chu, David Glickenstein, Christine Guenther, James Isenberg, Tom Ivey, Dan Knopf, Peng Lu, Feng Luo, Lei Ni Providence, Rhode Island American Mathematical Society [2015] xx, 374 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier Mathematical surveys and monographs volume 206 Mathematical surveys and monographs Chu, Sun-Chin Verfasser aut Glickenstein, David Verfasser aut (DE-604)BV022459869 4 Erscheint auch als Online-Ausgabe 978-1-4704-2677-4 Mathematical surveys and monographs volume 206 (DE-604)BV000018014 206 Digitalisierung UB Regensburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028737471&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Chow, Bennett 1962- Chu, Sun-Chin Glickenstein, David The Ricci Flow: techniques and applications Mathematical surveys and monographs |
| title | The Ricci Flow: techniques and applications |
| title_auth | The Ricci Flow: techniques and applications |
| title_exact_search | The Ricci Flow: techniques and applications |
| title_full | The Ricci Flow: techniques and applications IV Long-time solutions and related topics Bennett Chow, Sun-Chin Chu, David Glickenstein, Christine Guenther, James Isenberg, Tom Ivey, Dan Knopf, Peng Lu, Feng Luo, Lei Ni |
| title_fullStr | The Ricci Flow: techniques and applications IV Long-time solutions and related topics Bennett Chow, Sun-Chin Chu, David Glickenstein, Christine Guenther, James Isenberg, Tom Ivey, Dan Knopf, Peng Lu, Feng Luo, Lei Ni |
| title_full_unstemmed | The Ricci Flow: techniques and applications IV Long-time solutions and related topics Bennett Chow, Sun-Chin Chu, David Glickenstein, Christine Guenther, James Isenberg, Tom Ivey, Dan Knopf, Peng Lu, Feng Luo, Lei Ni |
| title_short | The Ricci Flow: techniques and applications |
| title_sort | the ricci flow techniques and applications long time solutions and related topics |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028737471&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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