Science China Mathematics

, Volume 61, Issue 8, pp 1421–1436 | Cite as

Functional inequalities on manifolds with non-convex boundary

  • Lijuan Cheng
  • Anton Thalmaier
  • James Thompson


In this article, new curvature conditions are introduced to establish functional inequalities including gradient estimates, Harnack inequalities and transportation-cost inequalities on manifolds with non-convex boundary.


Ricci curvature gradient inequality log-Sobolev inequality geometric flow 


60J60 58J65 53C44 



This work was supported by Fonds National de la Recherche Luxembourg (Grant No. O14/7628746 GEOMREV) and the University of Luxembourg (Grant No. IRP R-AGR-0517-10/AGSDE). The first author was supported by National Natural Science Foundation of China (Grant No. 11501508) and Zhejiang Provincial Natural Science Foundation of China (Grant No. LQ16A010009).


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Copyright information

© Science China Press and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Lijuan Cheng
    • 1
    • 2
  • Anton Thalmaier
    • 1
  • James Thompson
    • 1
  1. 1.Mathematics Research UnitUniversity of LuxembourgEsch-sur-AlzetteLuxembourg
  2. 2.Department of Applied MathematicsZhejiang University of TechnologyHangzhouChina

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