A Poincaré cone condition in the Poincaré group (Q1949219)

In the first part of this article, the author extends the derivation of Green kernel estimates for sub-elliptic diffusions obtained by \textit{G. Ben Arous} and \textit{M. Gradinaru} [Potential Anal. 8, No. 3, 217--258 (1998; Zbl 0909.60058)] to general hypoelliptic diffusions on a smooth manifold. In the second part, a Wiener regularity criterion and a Poincaré cone regularity condition are obtained for relativistic diffusions taking values in the Poincaré group of affine direct isometries of the Minkowski space-time.