Abstract
We prove new Beckner–Sobolev type inequalities on compact Kähler manifolds with positive Ricci curvature. As an application, we obtain a diameter upper bound that improves the Bonnet–Myers bound.
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Acknowledgements
It is our pleasure to thank Xiaodong Wang and Jiaping Wang for useful discussions and for their interest in this work. The first author was partially supported by NSF Grant DMS-1660031 and the Simons Foundation. The second author was partially supported by NSF Grant DMS-1506220.
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Baudoin, F., Munteanu, O. Improved Beckner–Sobolev Inequalities on Kähler Manifolds. J Geom Anal 31, 100–125 (2021). https://doi.org/10.1007/s12220-019-00252-w
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DOI: https://doi.org/10.1007/s12220-019-00252-w