collaborators

8 papers

math.CV2026

A bounded globally univalent quasiconformal harmonic map whose analytic part is unbounded

David Kalaj

We construct, for every \(0<k<1\), a bounded globally univalent harmonic mapping \[ f=h+\overline g \colon \D\to\C \] such that \[ |g'(z)|\le k|h'(z)|,\qquad z\in\D, \] while the a…

math.CV2026

The Norm of the Interior Cauchy Transform: Beyond the First Dirichlet Eigenvalue

David Kalaj

We study sharp \(L^2\) bounds for the interior Cauchy transform \(C_D\) on a bounded planar domain \(D\) and clarify its connection with the Dirichlet spectrum. We analyze an appro…

math.CV2026

The -Norm of the Cauchy transform on circular annuli

David Kalaj

We compute the exact operator norm of the Cauchy transform \[ (C_Ωf)(z)=\frac1π\int_Ω\frac{f(w)}{z-w}\,dA(w) \] on a circular annulus . Exploiting r…

math.AP2026

Lipschitz regularity of harmonic quasiconformal maps between Lyapunov domains in

Anton Gjokaj, David Kalaj

We prove that every sense-preserving harmonic --quasiconformal homeomorphism between Lyapunov domains (equivalently, bounded domains) in $\mathbb{R}^…

math.DG2025

Minimal surfaces over the Pitot quadrilaterals

Vladimir Dragović, David Kalaj

We develop a fully explicit framework for constructing Scherk-type minimal graphs over the Pitot quadrilaterals (i.e. such that the two pairs of opposite sides have the same total…

math.CV2025

On generalized M. Riesz conjugate function theorem for harmonic mappings

Anton Gjokaj, David Kalaj, Djordjije Vujadinovic

Let be the Lesbegue space of complex-valued functions defined in the unit circle . In this paper, we address the prob…