Integral representation of the sub-elliptic heat kernel on the complex anti-de Sitter fibration

Fabrice Baudoin (1) , Nizar Demni (2)

1 Department of Mathematics
2 IRMAR - Institut de Recherche Mathématique de Rennes

We derive an integral representation for the subelliptic heat kernel of the complex anti-de Sitter fibration. Our proof is different from the one used in Wang (Potential Anal 45:635–653, 2016) since it appeals to the commutativity of the D’Alembertian and of the Laplacian acting on the vertical variable rather than the analytic continuation of the heat semigroup of the real hyperbolic space. Our approach also sheds the light on the connection between the sub-Laplacian of the above fibration and the so-called generalized Maass Laplacian, and on the role played by the odd dimensional real hyperbolic space.

Mots clés: Anti-de Sitter fibration; Hyperbolic ball; Real hyperbolic space; Subelliptic heat kernel; Generalized Maass Laplacian

Domaines: Equations aux dérivées partielles [math.AP]

Fabrice Baudoin, Nizar Demni. Integral representation of the sub-elliptic heat kernel on the complex anti-de Sitter fibration. Archiv der Mathematik, 2018, 111 (4), pp.399 - 406. ⟨10.1007/s00013-018-1201-1⟩. ⟨hal-01882434⟩