Higher order asymptotic behavior of certain K\

Jae-Cheon Joo; Aeryeong Seo

doi:10.4134/JKMS.2015.52.1.113

Journal of the
Korean Mathematical Society JKMS

ISSN(Print) 0304-9914 ISSN(Online) 2234-3008

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J. Korean Math. Soc. 2015; 52(1): 113-124

Printed January 1, 2015

https://doi.org/10.4134/JKMS.2015.52.1.113

Higher order asymptotic behavior of certain K\"ahler metrics and uniformization for strongly pseudoconvex domains

Jae-Cheon Joo and Aeryeong Seo

University of Wuppertal, Korea Institute for Advanced Study (KIAS)

Abstract

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Abstract

We provide some relations between CR invariants of boundaries of strongly pseudoconvex domains and higher order asymptotic behavior of certain complete K\"ahler metrics of given domains. As a consequence, we prove a rigidity theorem of strongly pseudoconvex domains by asymptotic curvature behavior of metrics.

Keywords: Bergman metric, Graham-Lee connection, CR invariants

MSC numbers: 32V15, 53B35