Almost positive Ricci curvature in Kato sense — an extension of Myers’ theorem

It is shown that if the Kato constant of the negative part of the Ricci curvature below a positive level is small, then the volume of the corresponding manifold can be bounded above in terms of the Kato constant and the total Ricci curvature. Together with the results from [5] and [6], this yields a generalization of the famous Bonnet–Myers theorem. Connections to some earlier generalizations are discussed.

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Received 27 November 2019

Accepted 10 June 2021

Published 29 August 2022