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The Sharp Sobolev Inequality on Metric Measure Spaces with Lower Ricci Curvature Bounds

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Abstract

We show that the sharp Sobolev inequality as known for Riemannian manifolds with a positive lower bound on the Ricci curvature holds in the same form for metric measure spaces satisfying the RCD*(K, N) condition for positive K.

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Authors and Affiliations

  1. Institute for Applied Mathematics, University of Bonn, Endenicher Allee 60, 53115, Bonn, Germany

    Angelo Profeta

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  1. Angelo Profeta
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Profeta, A. The Sharp Sobolev Inequality on Metric Measure Spaces with Lower Ricci Curvature Bounds. Potential Anal 43, 513–529 (2015). https://doi.org/10.1007/s11118-015-9485-2

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