\(L^ p\)-pinching and the geometry of compact Riemannian manifolds. (English) Zbl 0821.53033

The authors prove a Harnack-type inequality for sections of Riemannian vector bundle over a compact manifold, lying in the kernel of a Schrödinger operator under \(L^ p\)-pinching assumptions on the potential.
Many geometric applications are given generalizing for example classical comparison results due to Bochner to the case of almost non-negative resp. non-positive Ricci curvature (in the sense of \(L^ p\)-estimates). Another application is that the minimal volume of an almost nonpositively curved manifold with infinite isometry group vanishes.


53C20 Global Riemannian geometry, including pinching
53C21 Methods of global Riemannian geometry, including PDE methods; curvature restrictions
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