Vanishing and finiteness results in geometric analysis: a generalization of the Bochner technique
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Basel [u.a.]
Birkhäuser
2008
|
| Series: | Progress in mathematics
266 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. 269 - 279 |
| Physical Description: | XIV, 282 S. 24 cm |
| ISBN: | 9783764386412 376438641X 9783764386429 |
Staff View
MARC
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| 100 | 1 | |a Pigola, Stefano |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Vanishing and finiteness results in geometric analysis |b a generalization of the Bochner technique |c Stefano Pigola ; Marco Rigoli ; Alberto G. Setti |
| 264 | 1 | |a Basel [u.a.] |b Birkhäuser |c 2008 | |
| 300 | |a XIV, 282 S. |c 24 cm | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Progress in mathematics |v 266 | |
| 500 | |a Literaturverz. S. 269 - 279 | ||
| 650 | 4 | |a Bochner, Technique de | |
| 650 | 4 | |a Riemann, Géométrie de | |
| 650 | 4 | |a Riemann, Variétés de | |
| 650 | 4 | |a Équations différentielles | |
| 650 | 4 | |a Bochner technique | |
| 650 | 4 | |a Differential equations | |
| 650 | 4 | |a Geometry, Riemannian | |
| 650 | 4 | |a Riemannian manifolds | |
| 650 | 0 | 7 | |a Bochner-Technik |0 (DE-588)4224695-7 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Geometrische Analysis |0 (DE-588)4156708-0 |2 gnd |9 rswk-swf |
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| 689 | 0 | 1 | |a Bochner-Technik |0 (DE-588)4224695-7 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Rigoli, Marco |e Verfasser |4 aut | |
| 700 | 1 | |a Setti, Alberto G. |e Verfasser |4 aut | |
| 830 | 0 | |a Progress in mathematics |v 266 |w (DE-604)BV000004120 |9 266 | |
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Record in the Search Index
| _version_ | 1804137716067074048 |
|---|---|
| adam_text | Contents
Introduction
vii
1
Harmonie,
pluriharmonic, holomorphic
maps
and basic Hermitian and
Kählerian
geometry
1
1.1
The general setting
........................... 1
1.2
The complex case
............................ 6
1.3
Hermitian
bundles
........................... 10
1.4
Complex geometry via moving
frames
................ 12
1.5 Weitzenböck-type
formulas
...................... 17
2
Comparison Results
27
2.1
Hessian and Laplacian comparison
.................. 27
2.2
Volume comparison and volume growth
............... 40
2.3
A monotonicity
formula for volumes
................. 58
3
Review of spectral theory
63
3.1
The spectrum of a self-adjoint operator
............... 63
3.2
Schrödinger
operators on Riemannian manifolds
........... 69
4
Vanishing results
83
4.1
Formulation of the problem
...................... 83
4.2
Liouville and vanishing results
.................... 84
4.3
Appendix: Chain rule under weak regularity
............. 99
5
A finite-dimensionality result
103
5.1
Peter Li s lemma
............................ 107
5.2
Poincaré-type
inequalities
....................... 110
5.3
Local Sobolev inequality
........................ 114
5.4
L2 Caccioppoli-type inequality
.................... 117
5.5
The
Moser
iteration procedure
.................... 118
5.6
A weak Harnack inequality
...................... 121
5.7
Proof of the abstract finiteness theorem
............... 122
6
Applications to harmonic maps
127
6.1
Harmonic maps of finite //-energy
.................. 127
6.2
Harmonic maps of bounded dilations and a Schwarz-type lemma
. 136
6.3
Fundamental group and harmonic maps
............... 141
6.4
A generalization of a finiteness theorem of Lemaire
......... 143
7
Some topologica!
applications
147
7.1
Ends and harmonic functions
..................... 147
7.2
Appendix: Further characterizations of parabolicity
......... 165
7.3
Appendix: The double of a Riemannian manifold
.......... 171
7.4
Topology at infinity of submanifolds of
C
-Н
spaces
......... 172
7.5
Line bundles over
Kahler
manifolds
.................. 178
7.6
Reduction of codimension of harmonic immersions
......... 179
8
Constancy of holomorphic maps and the structure of complete
Kahler
manifolds
183
8.1
Three versions of a result of Li and Yau
............... 183
8.2
Plurisubharmonic exhaustions
..................... 199
9
Splitting and gap theorems in the presence of
a Poincaré—
Sobolev
inequality
205
9.1
Splitting theorems
........................... 205
9.2
Gap theorems
.............................. 223
9.3
Gap Theorems, continued
....................... 229
A Unique continuation
235
В
ZAcohomology of non-compact manifolds
251
B.I The Lp
de Rham
cochain complex: reduced and unreduced
cohomologies
.............................. 251
B.2 Harmonic forms and L2-cohomology
................. 260
B.3 Harmonic forms and
L^^-cohomology................ 262
B.4 Some topological aspects of the theory
................ 265
Bibliography
269
Index
281
|
| adam_txt |
Contents
Introduction
vii
1
Harmonie,
pluriharmonic, holomorphic
maps
and basic Hermitian and
Kählerian
geometry
1
1.1
The general setting
. 1
1.2
The complex case
. 6
1.3
Hermitian
bundles
. 10
1.4
Complex geometry via moving
frames
. 12
1.5 Weitzenböck-type
formulas
. 17
2
Comparison Results
27
2.1
Hessian and Laplacian comparison
. 27
2.2
Volume comparison and volume growth
. 40
2.3
A monotonicity
formula for volumes
. 58
3
Review of spectral theory
63
3.1
The spectrum of a self-adjoint operator
. 63
3.2
Schrödinger
operators on Riemannian manifolds
. 69
4
Vanishing results
83
4.1
Formulation of the problem
. 83
4.2
Liouville and vanishing results
. 84
4.3
Appendix: Chain rule under weak regularity
. 99
5
A finite-dimensionality result
103
5.1
Peter Li's lemma
. 107
5.2
Poincaré-type
inequalities
. 110
5.3
Local Sobolev inequality
. 114
5.4
L2 Caccioppoli-type inequality
. 117
5.5
The
Moser
iteration procedure
. 118
5.6
A weak Harnack inequality
. 121
5.7
Proof of the abstract finiteness theorem
. 122
6
Applications to harmonic maps
127
6.1
Harmonic maps of finite //-energy
. 127
6.2
Harmonic maps of bounded dilations and a Schwarz-type lemma
. 136
6.3
Fundamental group and harmonic maps
. 141
6.4
A generalization of a finiteness theorem of Lemaire
. 143
7
Some topologica!
applications
147
7.1
Ends and harmonic functions
. 147
7.2
Appendix: Further characterizations of parabolicity
. 165
7.3
Appendix: The double of a Riemannian manifold
. 171
7.4
Topology at infinity of submanifolds of
C
-Н
spaces
. 172
7.5
Line bundles over
Kahler
manifolds
. 178
7.6
Reduction of codimension of harmonic immersions
. 179
8
Constancy of holomorphic maps and the structure of complete
Kahler
manifolds
183
8.1
Three versions of a result of Li and Yau
. 183
8.2
Plurisubharmonic exhaustions
. 199
9
Splitting and gap theorems in the presence of
a Poincaré—
Sobolev
inequality
205
9.1
Splitting theorems
. 205
9.2
Gap theorems
. 223
9.3
Gap Theorems, continued
. 229
A Unique continuation
235
В
ZAcohomology of non-compact manifolds
251
B.I The Lp
de Rham
cochain complex: reduced and unreduced
cohomologies
. 251
B.2 Harmonic forms and L2-cohomology
. 260
B.3 Harmonic forms and
L^^-cohomology. 262
B.4 Some topological aspects of the theory
. 265
Bibliography
269
Index
281 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Pigola, Stefano Rigoli, Marco Setti, Alberto G. |
| author_facet | Pigola, Stefano Rigoli, Marco Setti, Alberto G. |
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| author_sort | Pigola, Stefano |
| author_variant | s p sp m r mr a g s ag ags |
| building | Verbundindex |
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| callnumber-search | QA649 |
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| callnumber-subject | QA - Mathematics |
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| dewey-full | 516.3/62 516.362 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
| dewey-raw | 516.3/62 516.362 |
| dewey-search | 516.3/62 516.362 |
| dewey-sort | 3516.3 262 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
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| illustrated | Not Illustrated |
| index_date | 2024-07-02T21:06:57Z |
| indexdate | 2024-07-09T21:16:43Z |
| institution | BVB |
| isbn | 9783764386412 376438641X 9783764386429 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016539448 |
| oclc_num | 181090558 |
| open_access_boolean | |
| owner | DE-29T DE-355 DE-BY-UBR DE-19 DE-BY-UBM DE-824 DE-11 DE-83 DE-188 |
| owner_facet | DE-29T DE-355 DE-BY-UBR DE-19 DE-BY-UBM DE-824 DE-11 DE-83 DE-188 |
| physical | XIV, 282 S. 24 cm |
| publishDate | 2008 |
| publishDateSearch | 2008 |
| publishDateSort | 2008 |
| publisher | Birkhäuser |
| record_format | marc |
| series | Progress in mathematics |
| series2 | Progress in mathematics |
| spelling | Pigola, Stefano Verfasser aut Vanishing and finiteness results in geometric analysis a generalization of the Bochner technique Stefano Pigola ; Marco Rigoli ; Alberto G. Setti Basel [u.a.] Birkhäuser 2008 XIV, 282 S. 24 cm txt rdacontent n rdamedia nc rdacarrier Progress in mathematics 266 Literaturverz. S. 269 - 279 Bochner, Technique de Riemann, Géométrie de Riemann, Variétés de Équations différentielles Bochner technique Differential equations Geometry, Riemannian Riemannian manifolds Bochner-Technik (DE-588)4224695-7 gnd rswk-swf Geometrische Analysis (DE-588)4156708-0 gnd rswk-swf Geometrische Analysis (DE-588)4156708-0 s Bochner-Technik (DE-588)4224695-7 s DE-604 Rigoli, Marco Verfasser aut Setti, Alberto G. Verfasser aut Progress in mathematics 266 (DE-604)BV000004120 266 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016539448&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Pigola, Stefano Rigoli, Marco Setti, Alberto G. Vanishing and finiteness results in geometric analysis a generalization of the Bochner technique Progress in mathematics Bochner, Technique de Riemann, Géométrie de Riemann, Variétés de Équations différentielles Bochner technique Differential equations Geometry, Riemannian Riemannian manifolds Bochner-Technik (DE-588)4224695-7 gnd Geometrische Analysis (DE-588)4156708-0 gnd |
| subject_GND | (DE-588)4224695-7 (DE-588)4156708-0 |
| title | Vanishing and finiteness results in geometric analysis a generalization of the Bochner technique |
| title_auth | Vanishing and finiteness results in geometric analysis a generalization of the Bochner technique |
| title_exact_search | Vanishing and finiteness results in geometric analysis a generalization of the Bochner technique |
| title_exact_search_txtP | Vanishing and finiteness results in geometric analysis a generalization of the Bochner technique |
| title_full | Vanishing and finiteness results in geometric analysis a generalization of the Bochner technique Stefano Pigola ; Marco Rigoli ; Alberto G. Setti |
| title_fullStr | Vanishing and finiteness results in geometric analysis a generalization of the Bochner technique Stefano Pigola ; Marco Rigoli ; Alberto G. Setti |
| title_full_unstemmed | Vanishing and finiteness results in geometric analysis a generalization of the Bochner technique Stefano Pigola ; Marco Rigoli ; Alberto G. Setti |
| title_short | Vanishing and finiteness results in geometric analysis |
| title_sort | vanishing and finiteness results in geometric analysis a generalization of the bochner technique |
| title_sub | a generalization of the Bochner technique |
| topic | Bochner, Technique de Riemann, Géométrie de Riemann, Variétés de Équations différentielles Bochner technique Differential equations Geometry, Riemannian Riemannian manifolds Bochner-Technik (DE-588)4224695-7 gnd Geometrische Analysis (DE-588)4156708-0 gnd |
| topic_facet | Bochner, Technique de Riemann, Géométrie de Riemann, Variétés de Équations différentielles Bochner technique Differential equations Geometry, Riemannian Riemannian manifolds Bochner-Technik Geometrische Analysis |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016539448&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000004120 |
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