From Vanishing Theorems to Estimating Theorems: the Bochner Technique Revisited

Introduction Organization of the paper Sections A Basic Riemannian geometry B Examples of vanishing and estimating theorems C More Riemannian geometry D Proof of Theorem II E Bochner's theorem and estimating theorems in a more general setting F Proofs of the estimating theorems (sketch of) G From vanishing to estimating theorems : an account H Possible extensions of the methods I Final comments (geometric vs. analytic methods) Appendices I The isoperimetric profile II Using P. Li's lemma III Application of D. Meyer's lemma IV Using the heat equation V J. Moser's iteration scheme VI Sobolev embedding constants VII Symmetrization of elliptic or parabolic inequalities References