Kirill Lazebnik

collaborators

4 papers

math.CV2026

Blaschke Products Sharing a Welding Homeomorphism

Kirill Lazebnik

Given two Blaschke products $A$ , $B$ of the same degree, a \emph{welding homeomorphism} of $A$ , $B$ is a circle homeomorphism $k : T \to T$ satisfying $A\c…

math.CV2025

Sharp bounds for the valence of certain logharmonic polynomials

Kirill Lazebnik, Erik Lundberg

Consider a logharmonic polynomial; that is, a product of the form $p (z) q (z)$ , where $p$ , $q$ are holomorphic polynomials. Assume $q$ is linear and denote by $n$ the degr…

math.CV2025

Rational lemniscates and the matching problem

The matching problem for a given Jordan curve in the complex plane asks to find two nonconstant functions, one analytic in the bounded complementary component of the curve and the…

math.CV2025

On the Shapes of Rational Lemniscates

Christopher J. Bishop, Alexandre Eremenko, Kirill Lazebnik

A rational lemniscate is a level set of $∣ r ∣$ where $r : C^\to C^$ is rational. We prove that any planar Euler graph can be approximated, in a s…