Reference : Curvature-dimension inequalities on sub-Riemannian manifolds obtained from Riemannian...
Scientific journals : Article
Physical, chemical, mathematical & earth Sciences : Mathematics
http://hdl.handle.net/10993/18111
Curvature-dimension inequalities on sub-Riemannian manifolds obtained from Riemannian foliations: Part II
English
Grong, Erlend mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]
Thalmaier, Anton mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]
2016
Mathematische Zeitschrift
Springer
282
1
131-164
Yes
International
0025-5874
1432-1823
Berlin
Germany
[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.
Researchers ; Professionals
http://hdl.handle.net/10993/18111
10.1007/s00209-015-1535-3
http://front.math.ucdavis.edu/1408.6872

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