Families of conformally covariant differential operators, Q-curvatos and holography:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Basel [u.a.]
Birkhäuser
2009
|
| Series: | Progress in Mathematics
275 |
| Subjects: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018612020&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Physical Description: | XIII, 488 S. |
| ISBN: | 376439899X 9783764398996 |
Staff View
MARC
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| 100 | 1 | |a Juhl, Andreas |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Families of conformally covariant differential operators, Q-curvatos and holography |c Andreas Juhl |
| 264 | 1 | |a Basel [u.a.] |b Birkhäuser |c 2009 | |
| 300 | |a XIII, 488 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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| 490 | 1 | |a Progress in Mathematics |v 275 | |
| 650 | 4 | |a Differentialgeometrie - Riemannscher Raum - Differentialoperator - Krümmung | |
| 650 | 4 | |a Analysis of covariance | |
| 650 | 4 | |a Curvature | |
| 650 | 4 | |a Differential operators | |
| 650 | 4 | |a Geometry, Riemannian | |
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Record in the Search Index
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|---|---|
| adam_text | Contents
Preface
...................................... ix
1
Introduction
1.1
Hyperbolic geometry and
conformai
dynamics
........... 2
1.2
Automorphic distributions and intertwining families
....... 6
1.3
Asymptotically hyperbolic Einstein metrics.
Conformally covariant powers of the Laplacian
.......... 9
1.4
Intertwining families
......................... 11
1.5
The residue method for the hemisphere
............... 17
1.6
Q-curvature, holography and residue families
........... 20
1.7
Factorization of residue families. Recursive relations
....... 32
1.8
Families of conformally covariant differential operators
...... 42
1.9
Curved translation and tractor families
............... 46
1.10
Holographic duality. Extrinsic Q-curvature.
Odd order Q-curvature
........................ 50
1.11
Review of the contents
........................ 55
1.12
Some further perspectives
...................... 58
2
Spaces, Actions, Representations and Curvature
2.1
Lie groups, Lie algebras, spaces and actions
............ 63
2.2 Stereographic
projection
....................... 67
2.3
Poisson
transformations and spherical principal series
....... 71
2.4
The Nayatani metric
......................... 81
2.5
Riemannian curvature and
conformai
change
............ 82
3
Conformally Covariant Powers of the Laplacian, Q-curvature
and Scattering Theory
3.1
GJMS-operators and Q-curvature
.................. 87
3.2
Scattering theory
........................... 91
Contents
Paneitz Operator
and Paneitz Curvature
4.1 P4, Qi
and their transformation properties
............. 106
4.2
The fundamental identity for the Paneitz curvature
........ 108
4.3
Q4 and V4,
............................... 114
Intertwining Families
5.1
The algebraic theory
......................... 117
5.1.1
Even order families 2?2iv(A)
................. 117
5.1.2
Odd order families V2N+i
(λ)
................ 127
5.1.3
T>n( )
as
homomorphism of Verma modules
........ 129
5.2
Induced families
............................ 131
5.2.1
Induction
........................... 131
5.2.2
Even order families: D^(X) and
DţN{ )
......... 139
5.2.3
Odd order families: D^+1(X) and D2N+i(x)
.......
148
5.2.4
Eigenfunctions of
Δη»
and the families D jf(X)
...... 154
5.3
Some low order examples
...................... 161
5.4
Families for (R ,
S™ 1)
........................ 165
5.4.1
The families DbN(X)
..................... 165
5.4.2
D5(A), D|(A) and Db3{ )
................... 172
5.4.3
D|(0) for n = 4 and (P3,T) for (B4,S3)
.......... 176
5.5
Automorphic distributions
...................... 178
Conformally Covariant Families
6.1
Fundamental pairs and critical families
............... 190
6.2
The family Di(g; )
.......................... 194
6.3
D2(g;X) for a surface in a 3-manifold
................ 195
6.4
Second-order families. General case
................. 201
6.5
Families and the asymptotics of eigenfunctions
.......... 208
6.6
Residue families and holographic formulas for Q-curvature
.... 214
6.7
D2(g;X) as a residue family
..................... 235
6.8
DT3es(h;X)
............................... 236
6.9
The holographic coefficients V2,
va
and v%
............. 239
6.10
The holographic formula for Qq
................... 254
6.11
Factorization identities for residue families.
Recursive relations
.......................... 264
6.12
A recursive formula for P6. Universality
.............. 318
6.13
Recursive formulas for Qs and Pg
.................. 325
6.14
Holographic formula for conformally flat metrics
......... 329
6.15
va as a conformai
index density
................... 339
6.16
The holographic formula for Einstein metrics
........... 343
6.17
Semi-holonomic Verma modules and their role
........... 356
Contents
vii
6.18 Zuckerman
translation
and X>jv(A)
................. 360
6.19
From Verma modules to tractors
.................. 381
6.20
Some elements of tractor calculus
.................. 388
6.21
The tractor families Djf(M,T,-g;X)
................. 403
6.22
Some results on tractor families
................... 418
6.23
J
and Fialkow s fundamental forms
................ 445
6.24
£>2(<;;λ)
as a tractor family
..................... 450
6.25
The family
ϋξ {Μ
,Ћ;
g;
λ)
...................... 455
6.26
The pair (P3,Q3)
........................... 463
Bibliography
................................... 469
Index
....................................... 485
|
| any_adam_object | 1 |
| author | Juhl, Andreas |
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| author_role | aut |
| author_sort | Juhl, Andreas |
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| building | Verbundindex |
| bvnumber | BV035751981 |
| callnumber-first | Q - Science |
| callnumber-label | QA649 |
| callnumber-raw | QA649 |
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| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 370 |
| ctrlnum | (OCoLC)359673606 (DE-599)BVBBV035751981 |
| dewey-full | 516.373 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
| dewey-raw | 516.373 |
| dewey-search | 516.373 |
| dewey-sort | 3516.373 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV035751981 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-20T13:59:22Z |
| institution | BVB |
| isbn | 376439899X 9783764398996 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-018612020 |
| oclc_num | 359673606 |
| open_access_boolean | |
| owner | DE-355 DE-BY-UBR DE-83 |
| owner_facet | DE-355 DE-BY-UBR DE-83 |
| physical | XIII, 488 S. |
| publishDate | 2009 |
| publishDateSearch | 2009 |
| publishDateSort | 2009 |
| publisher | Birkhäuser |
| record_format | marc |
| series | Progress in Mathematics |
| series2 | Progress in Mathematics |
| spellingShingle | Juhl, Andreas Families of conformally covariant differential operators, Q-curvatos and holography Progress in Mathematics Differentialgeometrie - Riemannscher Raum - Differentialoperator - Krümmung Analysis of covariance Curvature Differential operators Geometry, Riemannian Differentialoperator (DE-588)4012251-7 gnd Krümmung (DE-588)4128765-4 gnd Differentialgeometrie (DE-588)4012248-7 gnd Riemannscher Raum (DE-588)4128295-4 gnd |
| subject_GND | (DE-588)4012251-7 (DE-588)4128765-4 (DE-588)4012248-7 (DE-588)4128295-4 |
| title | Families of conformally covariant differential operators, Q-curvatos and holography |
| title_auth | Families of conformally covariant differential operators, Q-curvatos and holography |
| title_exact_search | Families of conformally covariant differential operators, Q-curvatos and holography |
| title_full | Families of conformally covariant differential operators, Q-curvatos and holography Andreas Juhl |
| title_fullStr | Families of conformally covariant differential operators, Q-curvatos and holography Andreas Juhl |
| title_full_unstemmed | Families of conformally covariant differential operators, Q-curvatos and holography Andreas Juhl |
| title_short | Families of conformally covariant differential operators, Q-curvatos and holography |
| title_sort | families of conformally covariant differential operators q curvatos and holography |
| topic | Differentialgeometrie - Riemannscher Raum - Differentialoperator - Krümmung Analysis of covariance Curvature Differential operators Geometry, Riemannian Differentialoperator (DE-588)4012251-7 gnd Krümmung (DE-588)4128765-4 gnd Differentialgeometrie (DE-588)4012248-7 gnd Riemannscher Raum (DE-588)4128295-4 gnd |
| topic_facet | Differentialgeometrie - Riemannscher Raum - Differentialoperator - Krümmung Analysis of covariance Curvature Differential operators Geometry, Riemannian Differentialoperator Krümmung Differentialgeometrie Riemannscher Raum |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018612020&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000004120 |
| work_keys_str_mv | AT juhlandreas familiesofconformallycovariantdifferentialoperatorsqcurvatosandholography |