Vanishing and finiteness results in geometric analysis : a generalization of the Bochner technique
Author(s)
Bibliographic Information
Vanishing and finiteness results in geometric analysis : a generalization of the Bochner technique
（Progress in mathematics, v. 266）
Birkhäuser, c2008
Available at / 37 libraries
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Library, Research Institute for Mathematical Sciences, Kyoto University数研
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Note
Bibliography: p. [269]-279
Includes index
Description and Table of Contents
Description
This book describes 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.
Table of Contents
Harmonic, pluriharmonic, holomorphic maps and basic Hermitian and Kahlerian geometry.- Comparison Results.- Review of spectral theory.- Vanishing results.- A finite-dimensionality result.- Applications to harmonic maps.- Some topological applications.- Constancy of holomorphic maps and the structure of complete Kahler manifolds.- Splitting and gap theorems in the presence of a Poincare-Sobolev inequality.
by "Nielsen BookData"