From vanishing theorems to estimating theorems: The Bochner technique revisited. (English) Zbl 0662.53037
This is a highly interesting survey article about more recent developments of the Bochner technique. The author states estimating theorems extending the original vanishing results of Bochner. He sketches 3 methods of proof and gives details in a series of appendices.
Reviewer: U.Simon
MSC:
| 53C20 | Global Riemannian geometry, including pinching |
| 58J60 | Relations of PDEs with special manifold structures (Riemannian, Finsler, etc.) |
| 58J35 | Heat and other parabolic equation methods for PDEs on manifolds |
| 53-02 | Research exposition (monographs, survey articles) pertaining to differential geometry |
| 58-02 | Research exposition (monographs, survey articles) pertaining to global analysis |
| 58J50 | Spectral problems; spectral geometry; scattering theory on manifolds |
Keywords:
vanishing theorems; estimating theorems; Laplacian; Weitzenböck formulas; Kato inequalities; heat equation; maximum principle; Bochner techniqueReferences:
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