Logarithmic singularity of the Szegö kernel and a global invariant of strictly pseudoconvex domains

Details Logarithmic singularity of the Szegö kernel and a global invariant of strictly pseudoconvex domains Logarithmic singularity of the Szegö kernel and a global invariant of strictly pseudoconvex domains

2003-09-10

arxiv.org/abs/math/0309176v1

Ann. of Math. (2) 163 (2006), 499--515

Mathematics

Complex Variables

17 pages

Scientific paper

The Szego kernel of a strictly pseudoconvex domain admits a singularity on the boundary diagonal, which consists of a pole and logarithmic type singularity. In this paper, we prove that the integral over the boundary of the coefficient of the logarithmic singularity gives a biholomorphic invariant of a domain, or a CR invariant of the boundary. We also show that the same invariant appears as the coefficient of the logarithmic term of the volume expansion of the domain with respect to the Bergman volume element.

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