Verfügbarkeit: Vanishing and finiteness results in geometric analysis

Vanishing and finiteness results in geometric analysis: a generalization of the Bochner technique

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Bibliographische Detailangaben
Beteiligte Personen:	Pigola, Stefano (VerfasserIn), Rigoli, Marco (VerfasserIn), Setti, Alberto G. (VerfasserIn)
Format:	Buch
Sprache:	Englisch
Veröffentlicht:	Basel [u.a.] Birkhäuser 2008
Schriftenreihe:	Progress in mathematics 266
Schlagwörter:	Bochner, Technique de Riemann, Géométrie de Riemann, Variétés de Équations différentielles Bochner technique Differential equations Geometry, Riemannian Riemannian manifolds Bochner-Technik Geometrische Analysis
Links:	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
Beschreibung:	Literaturverz. S. 269 - 279
Umfang:	XIV, 282 S. 24 cm
ISBN:	9783764386412 376438641X 9783764386429

Internformat

MARC


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Datensatz im Suchindex

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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
any_adam_object	1
author	Pigola, Stefano Rigoli, Marco Setti, Alberto G.
author_facet	Pigola, Stefano Rigoli, Marco Setti, Alberto G.
author_role	aut aut aut
author_sort	Pigola, Stefano
author_variant	s p sp m r mr a g s ag ags
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ctrlnum	(OCoLC)181090558 (DE-599)DNB98575768X
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
format	Book
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id	DE-604.BV023355900
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indexdate	2024-12-20T13:14:22Z
institution	BVB
isbn	9783764386412 376438641X 9783764386429
language	English
oai_aleph_id	oai:aleph.bib-bvb.de:BVB01-016539448
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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
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_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
work_keys_str_mv	AT pigolastefano vanishingandfinitenessresultsingeometricanalysisageneralizationofthebochnertechnique AT rigolimarco vanishingandfinitenessresultsingeometricanalysisageneralizationofthebochnertechnique AT settialbertog vanishingandfinitenessresultsingeometricanalysisageneralizationofthebochnertechnique

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