Reference : Diffusion semigroup on manifolds with time-dependent metrics
 Document type : Scientific journals : Article Discipline(s) : Physical, chemical, mathematical & earth Sciences : Mathematics To cite this reference: http://hdl.handle.net/10993/22994
 Title : Diffusion semigroup on manifolds with time-dependent metrics Language : English Author, co-author : Cheng, Li Juan [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >] Publication date : Jul-2017 Journal title : Forum Mathematicum Publisher : Walter de Gruyter GmbH & Co. KG. Volume : 29 Issue/season : 4 Pages : 751-1002 Peer reviewed : Yes (verified by ORBilu) ISSN : 0933-7741 e-ISSN : 1435-5337 Keywords : [en] Functional inequalities ; Curvature ; Evolving metric Abstract : [en] Let $L_t:=\Delta_t +Z_t$, $t\in [0,T_c)$ on a differential manifold equipped with a complete geometric flow $(g_t)_{t\in [0,T_c)}$, where $\Delta_t$ is the Laplacian operator induced by the metric $g_t$ and $(Z_t)_{t\in [0,T_c)}$ is a family of $C^{1,\infty}$-vector fields. In this article, we present a number of equivalent inequalities for the lower bound curvature condition, which include gradient inequalities, transportation-cost inequalities, Harnack inequalities and other functional inequalities for the semigroup associated with diffusion processes generated by $L_t$. To this end, we establish the derivative formula for the associated semigroup and construct couplings for these diffusion processes by parallel displacement and reflection. Funders : Fonds National de la Recherche Luxembourg Name of the research project : O14/7628746 GEOMREV Target : Researchers ; Professionals Permalink : http://hdl.handle.net/10993/22994 DOI : 10.1515/forum-2015-0049 FnR project : FnR ; FNR7628746 > Anton Thalmaier > GEOMREV > Geometry Of Random Evolutions > 01/03/2015 > 28/02/2018 > 2014

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