3 citations · 4 across the 6 of their papers we have counts for
4 papers · 1 filter
A sharp bound on the number of self-intersections of a trigonometric curve
Sergei Kalmykov, Leonid V. Kovalev
We obtain a sharp bound on the number of self-intersections of a closed planar curve with trigonometric parameterization. Moreover, we show that a generic curve of this form is nor…
Bernstein- and Markov-type inequalities
Sergei Kalmykov, Béla Nagy, Vilmos Totik
This survey discusses the classical Bernstein and Markov inequalities for the derivatives of polynomials, as well as some of their extensions to general sets.
Continuity of logarithmic capacity
Sergei Kalmykov, Leonid V. Kovalev
We prove the continuity of logarithmic capacity under Hausdorff convergence of uniformly perfect planar sets. The continuity holds when the Hausdorff distance to the limit set tend…
Extremal decomposition problems for p-harmonic radius
Sergei Kalmykov, Elena Prilepkina
We extend classical results by Lavrent'ev and Kufarev concerning the product of the conformal radii of planar non-overlapping domains. We also extend relatively recent results for…