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CR Invariants of Weight Five in the Bergman Kernel

✍ Scribed by Kengo Hirachi; Gen Komatsu; Noriyuki Nakazawa

Publisher: Elsevier Science
Year: 1999
Tongue: English
Weight: 422 KB
Volume: 143
Category: Article
ISSN: 0001-8708
DOI: 10.1006/aima.1998.1794

No coin nor oath required. For personal study only.

✦ Synopsis

of getting a biholomorphically invariant asymptotic expansion of the Bergman kernel for smoothly bounded strictly pseudoconvex domains is realized in dimension 2 with the identification of universal constants. According to the program, the expansion is in terms of an approximately invariant smooth defining function of the domain, which we refer to as Fefferman's defining function, and the coefficients are functions in the domain constructed by using derivatives of Fefferman's defining function. Consequently, the invariant expansion is necessarily a finite sum with a remainder term and the ambiguity estimate is crucial in the problem. We get an expansion such that the boundary values of the coefficients are CR invariants of weight 5. This refines earlier results of C.

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