Vanishing and Finiteness Results in Geometric Analysis

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Vanishing and Finiteness Results in Geometric Analysis is written by Stefano Pigola and published by Springer Science & Business Media. It's available with International Standard Book Number or ISBN identification 3764386428 (ISBN 10) and 9783764386429 (ISBN 13).

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.