Inspired by the work of Z. Lu and G. Tian (Duke Math. J. 125:351–387, 2004) in the compact setting, in this paper we address the problem of studying the Szegö kernel of the disk bundle over a noncompact Kähler manifold. In particular we compute the Szegö kernel of the disk bundle over a Cartan–Hartogs domain based on a bounded symmetric domain. The main ingredients in our analysis are the fact that every Cartan–Hartogs domain can be viewed as an “iterated” disk bundle over its base and the ideas given in (Arezzo, Loi and Zuddas in Math. Z. 275:1207–1216, 2013) for the computation of the Szegö kernel of the disk bundle over an Hermitian symmetric space of compact type.
The first author was supported by Prin 2010/11—Varietà reali e complesse: geometria, topologia e analisi armonica—Italy; the third author was supported by the project FIRB “Geometria Differenziale e teoria geometrica delle funzioni”. All the authors were supported by INdAM-GNSAGA—Gruppo Nazionale per le Strutture Algebriche, Geometriche e le loro Applicazioni.
"On the Szegö kernel of Cartan–Hartogs domains." Ark. Mat. 54 (2) 473 - 484, October 2016. https://doi.org/10.1007/s11512-015-0228-9