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


Authors: Christian Rose and Peter Stollmann
Journal: Proc. Amer. Math. Soc. 145 (2017), 2199-2210
MSC (2010): Primary 53C21
DOI: https://doi.org/10.1090/proc/13399
Published electronically: January 23, 2017
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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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Additional Information

Christian Rose
Affiliation: Technische Universität Chemnitz, Faculty of Mathematics, D - 09107 Chemnitz, Germany

Peter Stollmann
Affiliation: Technische Universität Chemnitz, Faculty of Mathematics, D - 09107 Chemnitz, Germany

DOI: https://doi.org/10.1090/proc/13399
Received by editor(s): January 27, 2016
Received by editor(s) in revised form: May 12, 2016, and July 6, 2016
Published electronically: January 23, 2017
Communicated by: Guofang Wei
Article copyright: © Copyright 2017 American Mathematical Society