Article (Scientific journals)
Diffusion semigroup on manifolds with time-dependent metrics
Cheng, Li Juan
2017In Forum Mathematicum, 29 (4), p. 751-1002
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Keywords :
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.
Disciplines :
Mathematics
Author, co-author :
Cheng, Li Juan ;  University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit
External co-authors :
no
Language :
English
Title :
Diffusion semigroup on manifolds with time-dependent metrics
Publication date :
July 2017
Journal title :
Forum Mathematicum
ISSN :
1435-5337
Publisher :
Walter de Gruyter GmbH & Co. KG.
Volume :
29
Issue :
4
Pages :
751-1002
Peer reviewed :
Peer Reviewed verified by ORBi
FnR Project :
FNR7628746 - Geometry Of Random Evolutions, 2014 (01/03/2015-28/02/2018) - Anton Thalmaier
Name of the research project :
O14/7628746 GEOMREV
Funders :
Fonds National de la Recherche Luxembourg
Available on ORBilu :
since 15 December 2015

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