Open AccessAbstract Bergman kernel expansion and its applications
Author(s) -
Chiung-ju Liu,
Zhiqin Lu
Publication year - 2015
Publication title -
transactions of the american mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.798
H-Index - 100
eISSN - 1088-6850
pISSN - 0002-9947
DOI - 10.1090/tran/6621
Subject(s) - bergman kernel , mathematics , remainder , kernel (algebra) , polynomial , pure mathematics , mathematical analysis , arithmetic
We give a purely complex geometric proof of the existence of the Bergman kernel expansion. Our method actually provides a sharper estimate, and in the case that the metrics are real analytic, we prove that the remainder decays faster than any polynomial.