Hypocoercivity of Langevin-type dynamics on abstract smooth manifolds

In this article we investigate hypocoercivity of Langevin-type dynamics in nonlinear smooth geometries. The main result stating exponential decay to an equilibrium state with explicitly computable rate convergence is rooted appealing Hilbert space strategy by Dolbeault, Mouhot and Schmeiser. This was extended Grothaus Stilgenbauer (2014) Kolmogorov backward evolution equations contrast the dual Fokker–Planck framework. We use mathematically complete elaboration wide ranging classes SDEs abstract manifold setting, i.e. (at least) position variables obey certain side conditions. Such occur e.g. as fibre lay-down processes industrial applications. contribute Lagrangian-type formulation such geometric Langevin terms (semi-)sprays end L2-exponential ergodicity explicit rates for associated Hunt processes.