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Generalized Curvature Condition for Subelliptic Diffusion Processes
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Generalized Curvature Condition for Subelliptic Diffusion Processes
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By using a general version of curvature condition, derivative inequalities are established for a large class of subelliptic diffusion semigroups. As applications, the Harnack/cost-entropy/cost-variance inequalities for the diffusion semigroups, and the Poincar\'e/log-Sobolev inequalities for the associated Dirichlet forms in the symmetric case, are derived. Our results largely generalize and partly improve the corresponding ones obtained recently in [BB].
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Cited by 1 Pith paper
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Convergence to equilibrium for hypoelliptic non-symmetric Ornstein-Uhlenbeck type operators
Generalized curvature-dimension inequality for non-symmetric subelliptic Ornstein-Uhlenbeck operators yields L2 and entropic convergence to equilibrium, applying to two-step Carnot groups.
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