- journal article metadata
European Mathematical Society Publishing House
2016-09-19 17:05:47
Revista Matemática Iberoamericana
Rev. Mat. Iberoamericana
RMI
0213-2230
2235-0616
General
10.4171/RMI
http://www.ems-ph.org/doi/10.4171/RMI
subscribers
European Mathematical Society Publishing House
Zuerich, Switzerland
© European Mathematical Society (from 2012)
30
2014
1
Sobolev, Poincaré, and isoperimetric inequalities for subelliptic diffusion operators satisfying a generalized curvature dimension inequality
Fabrice
Baudoin
Purdue University, WEST LAFAYETTE, UNITED STATES
Bumsik
Kim
Purdue University, WEST LAFAYETTE, UNITED STATES
Sobolev inequalities, isoperimetric inequality, Poincaré inequality, subelliptic operator
By adapting some ideas of M. Ledoux ([12], [13] and [14]) to a sub-Riemannian framework we study Sobolev, Poincaré and isoperimetric inequalities associated to subelliptic diffusion operators that satisfy the generalized curvature dimension inequality that was introduced by F. Baudoin and N. Garofalo in [3]. Our results apply in particular on all CR Sasakian manifolds whose horizontal Webster–Tanaka–Ricci curvature is nonnegative, all Carnot groups with step two, and wide subclasses of principal bundles over Riemannian manifolds whose Ricci curvature is nonnegative.
Global analysis, analysis on manifolds
Partial differential equations
109
131
10.4171/RMI/771
http://www.ems-ph.org/doi/10.4171/RMI/771