Nikolai Nikolov

The Lempert function of the symmetrized polydisc in higher dimensions is not a distance

We prove that the Lempert function of the symmetrized polydisc in dimension greater than two is not a distance.

Behavior of the Bergman kernel and metric near convex boundary points

The boundary behavior of the Bergman metric near a convex boundary point z 0 of a pseudoconvex domain D C C is studied. It turns out that the Bergman metric at points z ∈ D in the direction of a fixed vector X 0 E C n tends to infinity, when z is approaching z 0 , if and only if the boundary of D does not contain any analytic disc through z 0 in the direction of X 0 .

Estimates of the Kobayashi and quasi-hyperbolic distances

Universal upper bounds for the Kobayashi and quasi-hyperbolic distances near Dini-smooth boundary points of domains in

The Kobayashi balls of C-convex domains

{{\mathbb {C}}}^n

ON THE DEFINITION OF THE KOBAYASHI–BUSEMAN PSEUDOMETRIC

Cn and

Lifting Maps from the Symmetrized Polydisc in Small Dimensions

{\mathbb {R}}^n