Let P be a real-valued and weighted homogeneous plurisubharmonic polynomial in $ℂ^{n-1}$ and let D denote the "model domain" {z ∈ ℂⁿ | r(z):= Re z₁ + P(z') < 0}. We prove a lower estimate on the Bergman distance of D if P is assumed to be strongly plurisubharmonic away from the coordinate axes.
2
Dostęp do pełnego tekstu na zewnętrznej witrynie WWW
We study the class of smooth bounded weakly pseudoconvex domains D ⊂ ℂⁿ whose boundary points are of finite type (in the sense of J. Kohn) and whose Levi form has at most one degenerate eigenvalue at each boundary point, and prove effective estimates on the invariant distance of Carathéodory. This completes the author's investigations on invariant differential metrics of Carathéodory, Bergman, and Kobayashi in the corank one situation and on invariant distances on pseudoconvex finite type domains in dimension two.
3
Dostęp do pełnego tekstu na zewnętrznej witrynie WWW
Let a and m be positive integers such that 2a < m. We show that in the domain $D:= {z ∈ ℂ³ | r(z):= ℜ z₁ + |z₁|² + |z₂|^{2m} + |z₂z₃|^{2a} + |z₃|^{2m} <0}$ the holomorphic sectional curvature $R_D(z;X)$ of the Bergman metric at z in direction X tends to -∞ when z tends to 0 non-tangentially, and the direction X is suitably chosen. It seems that an example with this feature has not been known so far.
4
Dostęp do pełnego tekstu na zewnętrznej witrynie WWW
We study the behavior of the pluricomplex Green function on a bounded hyperconvex domain D that admits a smooth plurisubharmonic exhaustion function ψ such that 1/|ψ| is integrable near the boundary of D, and moreover satisfies the estimate $|ψ| ≤ Cexp(-C'(log(1/δ_D))^α)$ at points close enough to the boundary with constants C,C' > 0 and 0 < α < 1. Furthermore, we obtain a Hopf lemma for such a function ψ. Finally, we prove a lower bound on the Bergman distance on D.
5
Dostęp do pełnego tekstu na zewnętrznej witrynie WWW
Let D be a smooth bounded pseudoconvex domain in ℂⁿ of finite type. We prove an estimate on the pluricomplex Green function $𝒢_D(z,w)$ of D that gives quantitative information on how fast the Green function vanishes if the pole w approaches the boundary. Also the Hölder continuity of the Green function is discussed.
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.