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Sharp p-Poincaré inequalities under measure contraction property

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Abstract

We obtain sharp estimate on p-spectral gaps, or equivalently optimal constant in p-Poincaré inequalities, for metric measure spaces satisfying measure contraction property. We also prove the rigidity for the sharp p-spectral gap.

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Acknowledgements

This research is part of a project which has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (Grant Agreement No. 637851). The author thanks Emanuel Milman for helpful discussions and comments.

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  1. Department of Mathematics, Technion-Israel Institute of Technology, Haifa, Israel

    Bang-Xian Han

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Correspondence to Bang-Xian Han.

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Han, BX. Sharp p-Poincaré inequalities under measure contraction property. manuscripta math. 162, 457–471 (2020). https://doi.org/10.1007/s00229-019-01138-5

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  • DOI: https://doi.org/10.1007/s00229-019-01138-5

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