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This article is concerned with maximal accretive realizations of geometricKramers-Fokker-Planck operators on manifolds with boundaries. A general classof boundary conditions is introduced which ensures the maximal accretivity andsome global subelliptic estimates. Those estimates imply nice spectralproperties as well as exponential decay properties for the associatedsemigroup. Admissible boundary conditions cover a wide range of applicationsfor the usual scalar Kramer-Fokker-Planck equation or Bismut's hypoellipticLaplacian.

Boundary conditions and subelliptic estimates for geometric Kramers-Fokker-Planck operators on manifolds with boundaries