Potential Analysis

, Volume 43, Issue 3, pp 513–529 | Cite as

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

Article

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.

Keywords

Sharp Sobolev inequality Nash inequality Metric measure spaces Curvature-dimension condition 

Mathematics Subject Classification (2010)

53C23 53C21 26D10 49J52 

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Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  1. 1.Institute for Applied MathematicsUniversity of BonnBonnGermany

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