Article (Scientific journals)
Functional inequalities on path space of sub-Riemannian manifolds and applications
Cheng, Li Juan; Grong, Erlend; Thalmaier, Anton
2021In Nonlinear Analysis: Theory, Methods and Applications, 210 (112387), p. 1-30
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Abstract :
[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 Poincaré inequality. As a consequence, we also obtain a bound for the spectral gap of the Ornstein-Uhlenbeck operator.
Disciplines :
Mathematics
Author, co-author :
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
External co-authors :
yes
Language :
English
Title :
Functional inequalities on path space of sub-Riemannian manifolds and applications
Publication date :
September 2021
Journal title :
Nonlinear Analysis: Theory, Methods and Applications
ISSN :
0362-546X
Publisher :
Elsevier, Oxford, United Kingdom
Volume :
210
Issue :
112387
Pages :
1-30
Peer reviewed :
Peer reviewed
FnR Project :
FNR7628746 - Geometry Of Random Evolutions, 2014 (01/03/2015-28/02/2018) - Anton Thalmaier
Name of the research project :
R-AGR-0517 - IRP15 - AGSDE (20150901-20190630) - THALMAIER Anton
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