# Some remarks on the Kobayashi--Fuks metric on strongly pseudoconvex domains

@inproceedings{Borah2021SomeRO, title={Some remarks on the Kobayashi--Fuks metric on strongly pseudoconvex domains}, author={Diganta Borah and Debaprasanna Kar}, year={2021} }

The Ricci curvature of the Bergman metric on a bounded domain D ⊂ C is strictly bounded above by n+ 1 and consequently log(K D gB,D), where KD is the Bergman kernel for D on the diagonal and gB,D is the Riemannian volume element of the Bergman metric on D, is the potential for a Kähler metric on D known as the Kobayashi–Fuks metric. In this note we study the localization of this metric near holomorphic peak points and also show that this metric shares several properties with the Bergman metric…

## References

SHOWING 1-10 OF 20 REFERENCES

On completeness of the Bergman metric and its subordinate metric.

- Mathematics, MedicineProceedings of the National Academy of Sciences of the United States of America
- 1976

It is proved that on any bounded domain in the complex Euclidean space C(n) the Bergman metric is always greater than or equal to the Carathéodory distance. This leads to a number of interesting…

Boundary behavior of the Bergman curvature in strictly pseudoconvex polyhedral domains.

- Mathematics
- 1996

In this article, we present an explicit description of the boundary behavior of the holomorphic curvature of the Bergman metric of bounded strictly pseudoconvex polyhedral domains with piecewise C2…

Deformation of complex structures, estimates for the ∂ equation, and stability of the Bergman kernel

- Mathematics
- 1982

The purpose of this paper is to investigate the stability, under perturbation of the boundary or ,of the complex structure, of the solutions to the $ Neumann problem on smoothly bounded strongly…

On the completeness of a metric related to the Bergman metric

- Mathematics
- 2012

We study the completeness of a metric which is related to the Bergman metric of a bounded domain (sometimes called the Burbea metric or Fuks metric). We provide a criterion for its completeness in…

Geometry of bounded domains

- Mathematics
- 1959

Some elementary properties of the kernel form and the Bergman metric (mostly already classical) are studied for the sake of completeness. Then we reexamine the theorem of H. Cartan on the group of…

Boundary behavior of the Carathéodory and Kobayashi metrics on strongly pseudoconvex domains in C[n] with smooth boundary

- Mathematics
- 1975

The Carathe'odory and Kobayashi distance functions on a bounded domain G in Cn have related infinitesimal forms. These are the Caratheodory and Kobayashi metrics. They are denoted by F(z, t) Oength…

On the Bergman invariant and curvatures of the Bergman metric

- Mathematics
- 1996

It is easy to see that both J and Rn are invariant under biholomorphic mappings. There-is an intrinsic relation between these two invariants; details are provided in Proposition 2.1. The invariant J…

Mesures de Monge-Ampère et mesures pluriharmoniques

- Mathematics
- 1987

— Let Ω be a bounded hyperconvex open subset in a Stein manifold. We study the properties of the “pluricomplex Green function” of Ω , denoted by uz(ζ) , solving the Dirichlet problem for the complex…

On the Bergman representative coordinates

- Mathematics
- 2011

We study the set where the so-called Bergman representative coordinates (or Bergman functions) form an immersion. We provide an estimate of the size of a maximal geodesic ball with respect to the…

An introduction to complex analysis in several variables

- Mathematics
- 1973

I. Analytic Functions of One Complex Variable. II. Elementary Properties of Functions of Several Complex Variables. III. Applications to Commutative Banach Algebras. IV. L2 Estimates and Existence…