Article (Scientific journals)
Curvature-dimension inequalities on sub-Riemannian manifolds obtained from Riemannian foliations: Part II
GRONG, Erlend; THALMAIER, Anton
2016In Mathematische Zeitschrift, 282 (1), p. 131-164
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Abstract :
[en] Using the curvature-dimension inequality proved in Part I, we look at consequences of this inequality in terms of the interaction between the sub-Riemannian geometry and the heat semi-group P_t corresponding to the sub-Laplacian. We give bounds for the gradient, entropy, a Poincaré inequality and a Li-Yau type inequality. These results require that the gradient of P_t f remains uniformly bounded whenever the gradient of f is bounded and we give several sufficient conditions for this to hold.
Disciplines :
Mathematics
Author, co-author :
GRONG, Erlend ;  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 :
Curvature-dimension inequalities on sub-Riemannian manifolds obtained from Riemannian foliations: Part II
Publication date :
2016
Journal title :
Mathematische Zeitschrift
ISSN :
0025-5874
eISSN :
1432-1823
Publisher :
Springer, Berlin, Germany
Volume :
282
Issue :
1
Pages :
131-164
Peer reviewed :
Peer Reviewed verified by ORBi
Available on ORBilu :
since 30 September 2014

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