Article (Scientific journals)
Characterization of pinched Ricci curvature by functional inequalities
CHENG, Li Juan; THALMAIER, Anton
2018In Journal of Geometric Analysis, 28 (3), p. 2312-2345
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Keywords :
Curvature; gradient estimate; log-Sobolev inequality
Abstract :
[en] In this article, functional inequalities for diffusion semigroups on Riemannian manifolds (possibly with boundary) are established, which are equivalent to pinched Ricci curvature, along with gradient estimates, L^p-inequalities and log-Sobolev inequalities. These results are further extended to differential manifolds carrying geometric flows. As application, it is shown that they can be used in particular to characterize general geometric flow and Ricci flow by functional inequalities.
Disciplines :
Mathematics
Author, co-author :
CHENG, Li Juan ;  University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit
THALMAIER, Anton ;  University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit
External co-authors :
no
Language :
English
Title :
Characterization of pinched Ricci curvature by functional inequalities
Publication date :
2018
Journal title :
Journal of Geometric Analysis
ISSN :
1559-002X
Publisher :
Springer New York LLC, New York, United States - New York
Volume :
28
Issue :
3
Pages :
2312-2345
Peer reviewed :
Peer Reviewed verified by ORBi
FnR Project :
FNR7628746 - Geometry Of Random Evolutions, 2014 (01/03/2015-28/02/2018) - Anton Thalmaier
Name of the research project :
R-AGR-0517 - IRP15 - AGSDE (20150901-20190630) - THALMAIER Anton
Funders :
University of Luxembourg - UL
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