## Remarks on the higher dimensional Suita conjecture

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- by G. P. Balakumar, Diganta Borah, Prachi Mahajan and Kaushal Verma PDF
- Proc. Amer. Math. Soc.
**147**(2019), 3401-3411 Request permission

## 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 $\mathbb {C}^2$.## References

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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
- 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
- © Copyright 2019 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**147**(2019), 3401-3411 - MSC (2010): Primary 32F45, 32A07, 32A25
- DOI: https://doi.org/10.1090/proc/14421
- MathSciNet review: 3981118