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.References
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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
- MR Author ID: 224163
- 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
- © Copyright 2017 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 145 (2017), 2199-2210
- MSC (2010): Primary 53C21
- DOI: https://doi.org/10.1090/proc/13399
- MathSciNet review: 3611331