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

• Main Authors: Pigola, Stefano, Rigoli, Marco, Setti, Alberto G
• Format: Book
• Language: English
• Published: Springer 2017
• Subjects: Mathematics; Statistics ; Riemannian manifolds ; Bochner technique ; Geometry, Riemannian; 516.362
• Online Access: http://repository.vnu.edu.vn/handle/VNU_123/30976
• Institution: Vietnam National University, Hanoi

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.