相关论文: Growth of Sibony metric and Bergman kernel for dom…

We generalize the inequality being a counterpart of the several complex variables version of the Suita conjecture. For this aim higher order generalizations of the Bergman kernel are introduced. As a corollary some new partial results on…

We study the lower bound for the Bergman kernel in terms of volume of sublevel sets of the pluricomplex Green function. We show that it implies a bound in terms of volume of the Azukawa indicatrix which can be treated as a multidimensional…

For a domain $D \subset \mathbb C^n$, $n \ge 2$, let $F^k_D(z)=K_D(z)\lambda\big(I^k_D(z)\big)$, 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…

We derive optimal estimates for the Bergman kernel and the Bergman metric for certain model domains in $\mathbb{C}^2$ near boundary points that are of infinite type. Being unbounded models, these domains obey certain geometric constraints…

The boundary behavior of the Bergman metric near a convex boundary point $z_0$ of a pseudoconvex domain $D\subset\CC^n$ is studied; it turns out that the Bergman metric at points $z\in D$ in direction of a fixed vector $X_0\in\CC^n$ tends…

We present a method of obtaining a lower bound estimate of the curvatures of the Bergman metric without using the regularity of the kernel function on the boundary. As an application, we prove the existence of an uniform lower bound of the…

In this paper we give an asymptotic expansion of the Bergman kernel for certain weakly pseudoconvex tube domains of finite type in C^2. Our asymptotic formula asserts that the singularity of the Bergman kernel at weakly pseudoconvex points…

We obtain a conceptually new differential geometric proof of P.F. Klembeck's result that the holomorphic sectional curvature of a strictly pseudoconvex domain approaches (in the boundary limit) the constant sectional curvature of the…

We use the Suita conjecture (now a theorem) to prove that for any domain $\Omega \subset \mathbb{C}$ its Bergman kernel $K(\cdot, \cdot)$ satisfies $K(z_0, z_0) = \hbox{Volume}(\Omega)^{-1}$ for some $z_0 \in \Omega$ if and only if $\Omega$…

We give an explicit lower bound, in terms of the distance from the boundary, for the Kobayashi metric of a certain class of bounded pseudoconvex domains in $\mathbb{C}^n$ with $\mathcal{C}^2$-smooth boundary using the regularity theory for…

In this paper, we first establish the localization of the Bergman kernels for unbounded pseudoconvex domains near a D'Angelo finite type boundary point. This result was proved by Engli\v{s} more than twenty years ago for bounded…

In this paper, we present an explicit description for the boundary behavior of the Bergman kernel function, the Bergman metric, and the associated curvatures along certain sequences converging to an $h$-extendible boundary point.

We study the problem of the boundary behaviour of the Bergman kernel and the Bergman completeness in some classes of bounded pseudoconvex domains, which contain also non-hyperconvex domains. Among the classes for which we prove the Bergman…

To study the analog of Suita's conjecture for domains $D \subset \mathbb{C}^n$, $n \ge 2$, B\l ocki 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…

We prove nontangential asymptotic limits of the Bergman kernel on the diagonal, and the Bergman metric and its holomorphic sectional curvature at exponentially flat infinite type boundary points of smooth bounded pseudoconvex domains in…

It is shown that the weak multidimensional Suita conjecture fails for any bounded non-pseudoconvex domain with $C^{1+\varepsilon_-}$-smooth boundary. On the other hand, it is proved that the weak converse to the Suita conjecture holds for…

Without using the $L^2$ extension theorem, we provide a new proof of the equality part in Suita's conjecture, which states that for any open Riemann surface admitting a Green's function, the Bergman kernel and the logarithmic capacity…

It is proved that for any domain in $\mathbb C^n$ the Caratheodory--Eisenman volume is comparable with the volume of the indicatrix of the Caratheodory metric up to small/large constants depending only on $n.$ Then the "multidimensional…

Carleson showed that the Bergman space for a domain on the plane is trivial if and only if its complement is polar. Here we give a quantitative version of this result. One is the Suita conjecture, established by the first-named author in…

We study the parameter dependence of the Bergman kernels on some planar domains depending on complex parameter \zeta in nontrivial "pseudoconvex" ways. Smoothly bounded cases are studied at first: It turns out that, in an example where the…