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A Poincaré Cone Condition in the Poincaré Group

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Abstract

Ben Arous and Gradinaru (Potential Anal 8(3):217–258, 1998) described the singularity of the Green function of a general sub-elliptic diffusion. In this article we first adapt their proof to the more general context of a hypoelliptic diffusion. In a second time, we deduce a Wiener criterion and a Poincaré cone condition for a relativistic diffusion with values in the Poincaré group (i.e the group of affine direct isometries of the Minkowski space-time).

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  1. Institut de Recherche Mathématique Avancée, Université de Strasbourg, Strasbourg, France

    Camille Tardif

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  1. Camille Tardif
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Tardif, C. A Poincaré Cone Condition in the Poincaré Group. Potential Anal 38, 1001–1030 (2013). https://doi.org/10.1007/s11118-012-9304-y

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