Remarks on the higher dimensional Suita conjecture
Authors:
G. P. Balakumar, Diganta Borah, Prachi Mahajan and Kaushal Verma
Journal:
Proc. Amer. Math. Soc. 147 (2019), 3401-3411
MSC (2010):
Primary 32F45, 32A07, 32A25
DOI:
https://doi.org/10.1090/proc/14421
Published electronically:
May 8, 2019
MathSciNet review:
3981118
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Abstract | References | Similar Articles | Additional Information
Abstract: To study the analog of Suita’s conjecture for domains $D \subset \mathbb {C}^n$, $n \geq 2$, Błocki introduced the invariant $F^k_D(z)=K_D(z)\lambda \big (I^k_D(z)\big )$, where $K_D(z)$ is the Bergman kernel of $D$ along the diagonal and $\lambda \big (I^k_D(z)\big )$ is the Lebesgue measure of the Kobayashi indicatrix at the point $z$. In this note, we study the behaviour of $F^k_D(z)$ (and other similar invariants using different metrics) on strongly pseudconvex domains and also compute its limiting behaviour explicitly at certain points of decoupled egg domains in $\mathbb {C}^2$.
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Additional Information
G. P. Balakumar
Affiliation:
Department of Mathematics, Indian Institute of Technology Palakkad, 678557, India
Email:
gpbalakumar@gmail.com
Diganta Borah
Affiliation:
Indian Institute of Science Education and Research, Pune 411008, India
Email:
dborah@iiserpune.ac.in
Prachi Mahajan
Affiliation:
Department of Mathematics, Indian Institute of Technology Bombay, Powai, Mumbai 400076, India
MR Author ID:
971599
Email:
prachi@math.iitb.ac.in
Kaushal Verma
Affiliation:
Department of Mathematics, Indian Institute of Science, Bangalore 560 012, India
MR Author ID:
650937
Email:
kverma@iisc.ac.in
Keywords:
Suita conjecture,
Bergman kernel,
Kobayashi indicatrix
Received by editor(s):
August 29, 2018
Received by editor(s) in revised form:
October 3, 2018
Published electronically:
May 8, 2019
Additional Notes:
The second-named author was partially supported by the DST-INSPIRE grant IFA-13 MA-21.
Communicated by:
Harold P. Boas
Article copyright:
© Copyright 2019
American Mathematical Society