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Field name	Details
Dewey Class	516.36
Title	Vanishing and Finiteness Results in Geometric Analysis ([EBook]) : A Generalization of the Bochner Technique / by Stefano Pigola, Alberto G. Setti, Marco Rigoli.
Author	Pigola, Stefano. , 1973-
Added Personal Name	Setti, Alberto G.
Added Personal Name	Rigoli, Marco
Other name(s)	SpringerLink (Online service)
Publication	Basel : Birkhäuser , 2008.
Physical Details	: online resource.
Series	Progress in mathematics ; 266
ISBN	9783764386429
Summary Note	This book presents very recent results involving an extensive use of analytical tools in the study of geometrical and topological properties of complete Riemannian manifolds. It analyzes in detail an extension of the Bochner technique to the non compact setting, yielding conditions which ensure that solutions of geometrically significant differential equations either are trivial (vanishing results) or give rise to finite dimensional vector spaces (finiteness results). The book develops a range of methods from spectral theory and qualitative properties of solutions of PDEs to comparison theorems in Riemannian geometry and potential theory. All needed tools are described in detail, often with an original approach. Some of the applications presented concern the topology at infinity of submanifolds, Lp cohomology, metric rigidity of manifolds with positive spectrum, and structure theorems for KÃ¤hler manifolds. The book is essentially self-contained and supplies in an original presentation the necessary background material not easily available in book form.:
Contents note	Introduction -- 1. Harmonic, pluriharmonic, holomorphic maps and basic Hermitian and KÃ¤hlerian geometry -- 2. Comparison Results -- 3. Review of spectral theory -- 4. Vanishing results -- 5. A finite-dimensionality result -- 6. Applications to harmonic maps -- 7. Some topological applications -- 8. Constancy of holomorphic maps and the structure of complete Kahler manifolds -- 9. Splitting and gap theorems in the presence of a PoincarÃ©-Sobolev inequality -- Appendices -- Bibliography -- Index.
System details note	Online resource is restricted to subscription institutions through IP address (only for SISSA users)
Internet Site	http://dx.doi.org/10.1007/978-3-7643-8642-9
Links to Related Works	Subject References: Analysis . Differential Geometry . Geometry, Differential . Global analysis . Global Analysis and Analysis on Manifolds . Global analysis (Mathematics) . Global differential geometry . Riemannian manifolds . Authors: author . Pigola, Stefano. 1973- . Rigoli, Marco . Setti, Alberto G. . Corporate Authors: SpringerLink (Online service) . Series: Progress in mathematics . Classification: 516.36 . 516.36 (DDC 23) .

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Vanishing and Finiteness Results in Geometric Analysis: A Generalization of the Bochner Technique

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