The analysis of harmonic maps and their heat flows:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Singapore [u.a.]
World Scientific
2008
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XI, 267 S. |
| ISBN: | 9789812779526 9812779523 |
Internformat
MARC
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| 100 | 1 | |a Lin, Fanghua |d 1959- |e Verfasser |0 (DE-588)121691241 |4 aut | |
| 245 | 1 | 0 | |a The analysis of harmonic maps and their heat flows |c Fanghua Lin ; Changyou Wang |
| 264 | 1 | |a Singapore [u.a.] |b World Scientific |c 2008 | |
| 300 | |a XI, 267 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 4 | |a Harmonic maps |v Textbooks | |
| 650 | 4 | |a Heat equation |v Textbooks | |
| 650 | 4 | |a Riemannian manifolds |v Textbooks | |
| 650 | 0 | 7 | |a Harmonische Abbildung |0 (DE-588)4023452-6 |2 gnd |9 rswk-swf |
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| 689 | 0 | 1 | |a Harmonische Abbildung |0 (DE-588)4023452-6 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Wang, Changyou |e Verfasser |4 aut | |
| 856 | 4 | 2 | |m Digitalisierung UB Bayreuth |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016592739&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-016592739 | ||
Datensatz im Suchindex
| _version_ | 1804137797519409152 |
|---|---|
| adam_text | Contents
Preface
vii
Organization of the book
ix
Acknowledgements
xi
1
Introduction to harmonic maps
1
1.1
Dirichlet principle of harmonic maps
.................. 1
1.2
Intrinsic view of harmonic maps
..................... 2
1.3
Extrinsic view of harmonic maps
.................... 3
1.4
A few facts about harmonic maps
.................... 4
1.5
Bochner identity for harmonic maps
.................. 5
1.6
Second variational formula of harmonic maps
............. 7
2
Regularity of minimizing harmonic maps
9
2.1
Minimizing harmonic maps in dimension two
............. 9
2.2
Minimizing harmonic maps in higher dimensions
........... 15
2.3
Federer s dimension reduction principle
................ 27
2.4
Boundary regularity for minimizing harmonic maps
.......... 31
2.5
Uniqueness of minimizing tangent maps
................ 35
2.6
Integrability of Jacobi fields and its applications
........... 40
3
Regularity of stationary harmonic maps
49
3.1
Weakly harmonic maps into regular balls
............... 49
3.2
Weakly harmonic maps in dimension two
............... 57
3.3
Stationary harmonic maps in higher dimensions
............ 64
3.4
Stable-stationary harmonic maps into spheres
............. 77
4
Blow up analysis of stationary harmonic maps
87
4.1
Preliminary analysis
........................... 87
4.2
Rectifiability of defect measures
..................... 94
4.3
Strong convergence and interior gradient estimates
.......... 101
4.4
Boundary gradient estimates
...................... 106
vi
CONTENTS
5
Heat flows to Riemannian manifolds of NPC
109
5.1
Motivation
................................ 109
5.2
Existence of short time smooth solutions
................ 110
5.3
Existence of global smooth solutions under KN
< 0.......... 113
5.4
An extension of Eells-Sampson s theorem
............... 118
6
Bubbling analysis in dimension two
125
6.1
Minimal immersion of spheres
...................... 126
6.2
Almost smooth heat flows in dimension two
.............. 134
6.3
Finite time singularity in dimension two
................ 141
6.4
Bubbling phenomena for 2-D heat flows
................ 144
6.5
Approximate harmonic maps in dimension two
............ 153
7
Partially smooth heat flows
161
7.1
Monotonicity
formula and a priori estimates
.............. 161
7.2
Global smooth solutions and weak compactness
............ 165
7.3
Finite time singularity in dimensions at least three
.......... 173
7.4
Nonuniqueness of heat flow of harmonic maps
............. 174
7.5
Global weak heat flows into spheres
................... 176
7.6
Global weak heat flows into general manifolds
............. 179
8
Blow up analysis on heat flows
189
8.1
Obstruction to strong convergence
................... 190
8.2
Basic estimates
.............................. 192
8.3
Stratification of the concentration set
.................. 197
8.4
Blow up analysis in dimension two
................... 204
8.5
Blow up analysis in dimensions
η
> 3 ................. 207
9
Dynamics of defect measures in heat flows
219
9.1
Generalized varifolds and rectifiability
................. 220
9.2
Generalized varifold flows and Brakke s motion
............ 231
9.3
Energy quantization of the defect measure
............... 239
9.4
Further remarks
............................. 249
Bibliography
251
Index
265
|
| adam_txt |
Contents
Preface
vii
Organization of the book
ix
Acknowledgements
xi
1
Introduction to harmonic maps
1
1.1
Dirichlet principle of harmonic maps
. 1
1.2
Intrinsic view of harmonic maps
. 2
1.3
Extrinsic view of harmonic maps
. 3
1.4
A few facts about harmonic maps
. 4
1.5
Bochner identity for harmonic maps
. 5
1.6
Second variational formula of harmonic maps
. 7
2
Regularity of minimizing harmonic maps
9
2.1
Minimizing harmonic maps in dimension two
. 9
2.2
Minimizing harmonic maps in higher dimensions
. 15
2.3
Federer's dimension reduction principle
. 27
2.4
Boundary regularity for minimizing harmonic maps
. 31
2.5
Uniqueness of minimizing tangent maps
. 35
2.6
Integrability of Jacobi fields and its applications
. 40
3
Regularity of stationary harmonic maps
49
3.1
Weakly harmonic maps into regular balls
. 49
3.2
Weakly harmonic maps in dimension two
. 57
3.3
Stationary harmonic maps in higher dimensions
. 64
3.4
Stable-stationary harmonic maps into spheres
. 77
4
Blow up analysis of stationary harmonic maps
87
4.1
Preliminary analysis
. 87
4.2
Rectifiability of defect measures
. 94
4.3
Strong convergence and interior gradient estimates
. 101
4.4
Boundary gradient estimates
. 106
vi
CONTENTS
5
Heat flows to Riemannian manifolds of NPC
109
5.1
Motivation
. 109
5.2
Existence of short time smooth solutions
. 110
5.3
Existence of global smooth solutions under KN
< 0. 113
5.4
An extension of Eells-Sampson's theorem
. 118
6
Bubbling analysis in dimension two
125
6.1
Minimal immersion of spheres
. 126
6.2
Almost smooth heat flows in dimension two
. 134
6.3
Finite time singularity in dimension two
. 141
6.4
Bubbling phenomena for 2-D heat flows
. 144
6.5
Approximate harmonic maps in dimension two
. 153
7
Partially smooth heat flows
161
7.1
Monotonicity
formula and a priori estimates
. 161
7.2
Global smooth solutions and weak compactness
. 165
7.3
Finite time singularity in dimensions at least three
. 173
7.4
Nonuniqueness of heat flow of harmonic maps
. 174
7.5
Global weak heat flows into spheres
. 176
7.6
Global weak heat flows into general manifolds
. 179
8
Blow up analysis on heat flows
189
8.1
Obstruction to strong convergence
. 190
8.2
Basic estimates
. 192
8.3
Stratification of the concentration set
. 197
8.4
Blow up analysis in dimension two
. 204
8.5
Blow up analysis in dimensions
η
> 3 . 207
9
Dynamics of defect measures in heat flows
219
9.1
Generalized varifolds and rectifiability
. 220
9.2
Generalized varifold flows and Brakke's motion
. 231
9.3
Energy quantization of the defect measure
. 239
9.4
Further remarks
. 249
Bibliography
251
Index
265 |
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| illustrated | Not Illustrated |
| index_date | 2024-07-02T21:27:13Z |
| indexdate | 2024-07-09T21:18:00Z |
| institution | BVB |
| isbn | 9789812779526 9812779523 |
| language | English |
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| physical | XI, 267 S. |
| publishDate | 2008 |
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| publisher | World Scientific |
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| spelling | Lin, Fanghua 1959- Verfasser (DE-588)121691241 aut The analysis of harmonic maps and their heat flows Fanghua Lin ; Changyou Wang Singapore [u.a.] World Scientific 2008 XI, 267 S. txt rdacontent n rdamedia nc rdacarrier Harmonic maps Textbooks Heat equation Textbooks Riemannian manifolds Textbooks Harmonische Abbildung (DE-588)4023452-6 gnd rswk-swf Wärmestrom (DE-588)4121893-0 gnd rswk-swf Wärmestrom (DE-588)4121893-0 s Harmonische Abbildung (DE-588)4023452-6 s DE-604 Wang, Changyou Verfasser aut Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016592739&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Lin, Fanghua 1959- Wang, Changyou The analysis of harmonic maps and their heat flows Harmonic maps Textbooks Heat equation Textbooks Riemannian manifolds Textbooks Harmonische Abbildung (DE-588)4023452-6 gnd Wärmestrom (DE-588)4121893-0 gnd |
| subject_GND | (DE-588)4023452-6 (DE-588)4121893-0 |
| title | The analysis of harmonic maps and their heat flows |
| title_auth | The analysis of harmonic maps and their heat flows |
| title_exact_search | The analysis of harmonic maps and their heat flows |
| title_exact_search_txtP | The analysis of harmonic maps and their heat flows |
| title_full | The analysis of harmonic maps and their heat flows Fanghua Lin ; Changyou Wang |
| title_fullStr | The analysis of harmonic maps and their heat flows Fanghua Lin ; Changyou Wang |
| title_full_unstemmed | The analysis of harmonic maps and their heat flows Fanghua Lin ; Changyou Wang |
| title_short | The analysis of harmonic maps and their heat flows |
| title_sort | the analysis of harmonic maps and their heat flows |
| topic | Harmonic maps Textbooks Heat equation Textbooks Riemannian manifolds Textbooks Harmonische Abbildung (DE-588)4023452-6 gnd Wärmestrom (DE-588)4121893-0 gnd |
| topic_facet | Harmonic maps Textbooks Heat equation Textbooks Riemannian manifolds Textbooks Harmonische Abbildung Wärmestrom |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016592739&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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