David Kalaj

collaborators

5 papers

math.AP2026

Lipschitz regularity of harmonic quasiconformal maps between Lyapunov domains in $R^{n}$

Anton Gjokaj, David Kalaj

We prove that every sense-preserving harmonic $K$ --quasiconformal homeomorphism $f : D \to Ω$ between Lyapunov domains (equivalently, bounded $C^{1, α}$ domains) in $R^{n}$ …

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 $L^{p} (T)$ be the Lesbegue space of complex-valued functions defined in the unit circle $T = {z : ∣ z ∣ = 1} \subseteq C$ . In this paper, we address the prob…

math.DG2025

On a sharp form of curvature conjecture for minimal graphs

David Kalaj

Recently, the author and Melentijević resolved the longstanding Gaussian curvature problem by proving the sharp inequality \[ |\mathcal{K}| < c_0 = \frac{π^2}{2} \] for minimal gra…

math.CV2025

Zygmund theorem for harmonic quasiregular mappings

David Kalaj

Let $K \geq 1$ . We prove Zygmund theorem for $K -$ quasiregular harmonic mappings in the unit disk $D$ in the complex plane by providing a constant $C (K)$ in the inequality $$…

Lipschitz regularity of harmonic quasiconformal maps between Lyapunov domains in Rn

Minimal surfaces over the Pitot quadrilaterals

On generalized M. Riesz conjugate function theorem for harmonic mappings

On a sharp form of curvature conjecture for minimal graphs

Zygmund theorem for harmonic quasiregular mappings

Lipschitz regularity of harmonic quasiconformal maps between Lyapunov domains in $R^{n}$