The Kato class on compact manifolds with integral bounds on the negative part of Ricci curvature

Rose, Christian; Stollmann, Peter

doi:10.1090/proc/13399

The Kato class on compact manifolds with integral bounds on the negative part of Ricci curvature
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by Christian Rose and Peter Stollmann PDF

Proc. Amer. Math. Soc. 145 (2017), 2199-2210 Request permission

Abstract:

We show that under Ricci curvature integral assumptions the dimension of the first cohomology group can be estimated in terms of the Kato constant of the negative part of the Ricci curvature. Moreover, this provides quantitative statements about the cohomology group, expanding results by Elworthy and Rosenberg.

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