| Functional inequalities on path space of sub-Riemannian manifolds and applications |

| English |

| Cheng, Li Juan *[Department of Applied Mathematics > Zhejiang University of Technology, Hangzhou]* |

| Grong, Erlend *[University of Bergen > Department of Mathematics]* |

| Thalmaier, Anton *[University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]* |

| Sep-2021 |

| Nonlinear Analysis: Theory, Methods and Applications |

| Elsevier |

| 210 |

| 112387 |

| 1-30 |

| Yes |

| International |

| 0362-546X |

| Oxford |

| UK |

| [en] We consider the path space of a manifold with a measure induced by a stochastic flow with an infinitesimal generator that is hypoelliptic, but not elliptic. These generators can be seen as sub-Laplacians of a sub-Riemannian structure with a chosen complement. We introduce a concept of gradient for cylindrical functionals on path space in such a way that the gradient operators are closable in L^2. With this structure in place, we show that a bound on horizontal Ricci curvature is equivalent to several inequalities for functions on path space, such as a gradient inequality, log-Sobolev inequality and PoincarĂ© inequality. As a consequence, we also obtain a bound for the spectral gap of the Ornstein-Uhlenbeck operator. |

| R-AGR-0517 > AGSDE > 01/09/2015 - 31/08/2018 > THALMAIER Anton |

| Researchers |

| http://hdl.handle.net/10993/41284 |

| 10.1016/j.na.2021.112387 |

| https://authors.elsevier.com/sd/article/S0362546X21000924 |

| FnR ; FNR7628746 > Anton Thalmaier > GEOMREV > Geometry of random evolutions > 01/03/2015 > 28/02/2018 > 2014 |