The analysis of harmonic maps and their heat flows:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Singapore [u.a.]
World Scientific
2008
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XI, 267 S. |
| ISBN: | 9789812779526 9812779523 |
Staff View
MARC
| LEADER | 00000nam a2200000 c 4500 | ||
|---|---|---|---|
| 001 | BV023410117 | ||
| 003 | DE-604 | ||
| 005 | 20250522 | ||
| 007 | t| | ||
| 008 | 080723s2008 xx |||| 00||| eng d | ||
| 020 | |a 9789812779526 |9 978-981-277-952-6 | ||
| 020 | |a 9812779523 |9 981-277-952-3 | ||
| 035 | |a (OCoLC)191658556 | ||
| 035 | |a (DE-599)HBZHT015532871 | ||
| 040 | |a DE-604 |b ger |e rakwb | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-20 |a DE-703 |a DE-355 |a DE-739 |a DE-11 |a DE-188 | ||
| 050 | 0 | |a QA614.73 | |
| 082 | 0 | |a 514/.74 |2 22 | |
| 084 | |a SK 370 |0 (DE-625)143234: |2 rvk | ||
| 084 | |a SK 540 |0 (DE-625)143245: |2 rvk | ||
| 084 | |a SK 660 |0 (DE-625)143251: |2 rvk | ||
| 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 |
| 650 | 0 | 7 | |a Wärmestrom |0 (DE-588)4121893-0 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Wärmestrom |0 (DE-588)4121893-0 |D s |
| 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 |0 (DE-588)1127342533 |4 aut | |
| 856 | 4 | |m Digitalisierung UB Bayreuth |u https://bvbr.bib-bvb.de:443/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016592739&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |z Inhaltsverzeichnis | |
| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-016592739 | |
Record in the Search Index
| _version_ | 1832829570758213632 |
|---|---|
| adam_text | |
| 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 |
| any_adam_object | |
| any_adam_object_boolean | 1 |
| author | Lin, Fanghua 1959- Wang, Changyou |
| author_GND | (DE-588)121691241 (DE-588)1127342533 |
| author_facet | Lin, Fanghua 1959- Wang, Changyou |
| author_role | aut aut |
| author_sort | Lin, Fanghua 1959- |
| author_variant | f l fl c w cw |
| building | Verbundindex |
| bvnumber | BV023410117 |
| callnumber-first | Q - Science |
| callnumber-label | QA614 |
| callnumber-raw | QA614.73 |
| callnumber-search | QA614.73 |
| callnumber-sort | QA 3614.73 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 370 SK 540 SK 660 |
| ctrlnum | (OCoLC)191658556 (DE-599)HBZHT015532871 |
| dewey-full | 514/.74 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 514 - Topology |
| dewey-raw | 514/.74 |
| dewey-search | 514/.74 |
| dewey-sort | 3514 274 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>00000nam a2200000 c 4500</leader><controlfield tag="001">BV023410117</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20250522</controlfield><controlfield tag="007">t|</controlfield><controlfield tag="008">080723s2008 xx |||| 00||| eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9789812779526</subfield><subfield code="9">978-981-277-952-6</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9812779523</subfield><subfield code="9">981-277-952-3</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)191658556</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)HBZHT015532871</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-20</subfield><subfield code="a">DE-703</subfield><subfield code="a">DE-355</subfield><subfield code="a">DE-739</subfield><subfield code="a">DE-11</subfield><subfield code="a">DE-188</subfield></datafield><datafield tag="050" ind1=" " ind2="0"><subfield code="a">QA614.73</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">514/.74</subfield><subfield code="2">22</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 370</subfield><subfield code="0">(DE-625)143234:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 540</subfield><subfield code="0">(DE-625)143245:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 660</subfield><subfield code="0">(DE-625)143251:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Lin, Fanghua</subfield><subfield code="d">1959-</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)121691241</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">The analysis of harmonic maps and their heat flows</subfield><subfield code="c">Fanghua Lin ; Changyou Wang</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Singapore [u.a.]</subfield><subfield code="b">World Scientific</subfield><subfield code="c">2008</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">XI, 267 S.</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Harmonic maps</subfield><subfield code="v">Textbooks</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Heat equation</subfield><subfield code="v">Textbooks</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Riemannian manifolds</subfield><subfield code="v">Textbooks</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Harmonische Abbildung</subfield><subfield code="0">(DE-588)4023452-6</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Wärmestrom</subfield><subfield code="0">(DE-588)4121893-0</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Wärmestrom</subfield><subfield code="0">(DE-588)4121893-0</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="1"><subfield code="a">Harmonische Abbildung</subfield><subfield code="0">(DE-588)4023452-6</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Wang, Changyou</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)1127342533</subfield><subfield code="4">aut</subfield></datafield><datafield tag="856" ind1="4" ind2=" "><subfield code="m">Digitalisierung UB Bayreuth</subfield><subfield code="u">https://bvbr.bib-bvb.de:443/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016592739&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="z">Inhaltsverzeichnis</subfield></datafield><datafield tag="943" ind1="1" ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-016592739</subfield></datafield></record></collection> |
| id | DE-604.BV023410117 |
| illustrated | Not Illustrated |
| index_date | 2024-07-02T21:27:13Z |
| indexdate | 2025-05-22T14:01:27Z |
| institution | BVB |
| isbn | 9789812779526 9812779523 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016592739 |
| oclc_num | 191658556 |
| open_access_boolean | |
| owner | DE-20 DE-703 DE-355 DE-BY-UBR DE-739 DE-11 DE-188 |
| owner_facet | DE-20 DE-703 DE-355 DE-BY-UBR DE-739 DE-11 DE-188 |
| physical | XI, 267 S. |
| publishDate | 2008 |
| publishDateSearch | 2008 |
| publishDateSort | 2008 |
| publisher | World Scientific |
| record_format | marc |
| 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 (DE-588)1127342533 aut Digitalisierung UB Bayreuth https://bvbr.bib-bvb.de:443/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 | https://bvbr.bib-bvb.de:443/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016592739&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT linfanghua theanalysisofharmonicmapsandtheirheatflows AT wangchangyou theanalysisofharmonicmapsandtheirheatflows |