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



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.


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

Mathematics Subject Classification

35H20 35K08 


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Authors and Affiliations

  1. 1.Department of MathematicsUniversity of ConnecticutMansfieldUSA
  2. 2.IRMARUniversité de Rennes 1Rennes CedexFrance

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