31 citations · 78 across the 39 of their papers we have counts for
39 papers · 1 filter
On left inverses in the Lempert theorem
Włodzimierz Zwonek
In the paper we discuss the problem of existence, uniqueness and extension through the boundary of left inverses to complex geodesics in Lempert domains. We concentrate on special…
Burns-Krantz rigidity in non-smooth domains
Włodzimierz Zwonek
Motivated by recent papers \cite{For-Rong 2021} and \cite{Ng-Rong 2024} we prove a boundary Schwarz lemma (Burns-Krantz rigidity type theorem) for non-smooth boundary points of the…
Isometries in the diamond
Anand Chavan, Włodzimierz Zwonek
We show the (anti)holomorphicity of smooth Kobayashi isometries of the diamond, the domain defined as . Additionally, we discuss the p…
Extension property in the tridisc
Lukasz Kosinski, Wlodzimierz Zwonek
Motivated by works on extension sets in standard domains we introduce a notion of the Carathéodory set that seems better suited for the methods used in proofs of results on charact…
Generalizations of the higher dimensional Suita conjecture and its relation with a problem of Wiegerinck
Wlodzimierz Zwonek, Zbigniew Blocki
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 a…
Function theoretic properties of symmetric powers of complex manifolds
Włodzimierz Zwonek
In the paper we study properties of symmetric powers of complex manifolds. We investigate a number of function theoretic properties (e. g. (quasi) -finite compactness, existence…
Peak functions in -convex domains
Peter Pflug, Wlodzimierz Zwonek
In the paper we show the existence of different types of peak functions in classes of -convex domains. As one of tools used in this context is a result on preserving the…
One dimensional estimates for the Bergman kernel and logarithmic capacity
Zbigniew Błocki, Włodzimierz Zwonek
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 S…
Regularity of complex geodesics and (non)-Gromov hyperbolicity of convex tube domains
Peter Pflug, Wlodzimierz Zwonek
We deliver examples of non-Gromov hyperbolic tube domains with convex bases (equipped with the Kobayashi distance). This is shown by providing a criterion on non-Gromov hyperbolici…
-functions in unbounded balanced domains
Peter Pflug, Wlodzimierz Zwonek
We investigate problems related with the existence of square integrable holomorphic functions on (unbounded) balanced domains. In particular, we solve the problem of Wiegerinck for…
Coman conjecture for the bidisc
Lukasz Kosinski, Pascal J. Thomas, Wlodzimierz Zwonek
In the paper we show the equality between the Lempert function and the Green function with two poles with equal weights in the bidisc thus giving the positive answer to a conjectur…
On the Suita conjecture for some convex ellipsoids in
Włodzimierz Zwonek, Zbigniew Błocki
It has been recently shown that for a convex domain in and the function , where is the Bergman kernel on th…
Estimates for the Bergman Kernel and the Multidimensional Suita Conjecture
Zbigniew Błocki, Włodzimierz Zwonek
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 Az…
Nevanlinna-Pick problem and uniqueness of left inverses in convex domains, symmetrized bidisc and tetrablock
Ł. Kosiński, W. Zwonek
In the paper we discuss the problem of uniqueness of left inverses (solutions of two point Nevanlinna-Pick problem) in bounded convex domains, strongly linearly convex domains, the…
Geometric properties of the tetrablock
Włodzimierz Zwonek
In this short note we show that the tetrablock is i $\C$-convex domain. In the proof of this fact a new class of ($\C$-convex) domains is studied. The domains are natural caniddate…
Proper holomorphic mappings vs. peak points and Silov boundary
W. Zwonek, L. Kosinski
We present a result on existence of some kind of peak functions for $\C$-convex domains and for the symmetrized polydisc. Then we apply the latter result to show the equivariance o…
Exhausting domains of the symmetrized bidisc
Peter Pflug, Wlodzimierz Zwonek
We show that the symmetrized bidisc may be exhausted by strongly linearly convex domains. It shows in particular the existence of a strongly linearly convex domain that cannot be e…
Green functions of the spectral ball and symmetrized polydisk
Pascal J. Thomas, Nguyen Van Trao, Wlodzimierz Zwonek
The Green function of the spectral ball is constant over the isospectral varieties, is never less than the pullback of its counterpart on the symmetrized polydisk, and is equal to…
Boundary behavior of the Kobayashi-Royden metric in smooth pseudoconvex domains
Peter Pflug, Włodzimierz Zwonek
We show some lower estimates for the Kobayashi-Royden metric on a class of smooth bounded pseudoconvex domains.
Asymptotic behaviour of the sectional curvature of the Bergman metric for annuli
Wlodzimierz Zwonek
We extend and simplify results of \cite{Din~2009} where the asymptotic behavior of the holomorphic sectional curvature of the Bergman metric in annuli is studied. Similarly as in \…
Estimates for invariant metrics on -convex domains
Nikolai Nikolov, Peter Pflug, Wlodzimierz Zwonek
Geometric lower and upper estimates are obtained for invariant metrics on -convex domains containing no complex lines.
On a local characterization of pseudoconvex domains
Nikolai Nikolov, Peter Pflug, Pascal J. Thomas +1
Pseudoconvexity of a domain in is described in terms of the existence of a locally defined plurisubharmonic/holomorphic function near any boundary point that is unbounde…
Discontinuity of the Lempert function and the Kobayashi--Royden metric of the spectral ball
Nikolai Nikolov, Pascal J. Thomas, Wlodzimierz Zwonek
Some results on the discontinuity properties of the Lempert function and the Kobayashi pseudometric in the spectral ball are given.
Proper holomorphic mappings of the spectral unit ball
Wlodzimierz Zwonek
We prove an Alexander type theorem for the spectral unit ball showing that there are no non-trivial proper holomorphic mappings in , .