Author

David Kalaj

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Preprint Sep 2026

On an Iwaniec--Kovalev--Onninen Conjecture for harmonic quasiconformal annulus mappings

In 2012, Iwaniec, Kovalev and Onninen proposed an upper Nitsche--Gr\"otzsch type estimate for harmonic $K$-quasiconformal homeomorphisms between circular annuli: in normalized form, every such map $h:A(1,s)\to A(1,S)$ should satisfy \[ S \leq \frac{K+1}{2}s-\frac{K-1}{2s}. \] The radial and spiral-radial one-mode model...

David Kalaj, Jin-Song Liu, Jian-Feng Zhu · 0 citations

Preprint Aug 2026

A Lewy-type theorem for pluriharmonic mappings in $\C^2$ and bi-Lipschitz quasiconformal harmonic maps

Lewy's theorem says that a one-to-one harmonic mapping between plane domains has nonvanishing Jacobian. In dimensions at least three this statement is false for general harmonic homeomorphisms. We prove a four-dimensional Lewy theorem under the additional complex-analytic assumption of pluriharmonicity. More precisely,...

David Kalaj · 1 citation · ⚡1

Preprint Jul 2026

The Gromov--Ros conjecture for rank-one symmetric spaces of noncompact type

We prove the Gromov--Ros conjecture for every rank-one symmetric space of noncompact type: finite-perimeter isoperimetric regions are precisely the geodesic balls, up to ambient isometry and null sets. The proof is organized uniformly in the root multiplicities $(p,q)$. We introduce the volume radius \[ R(r)^n=n\int_0^...

David Kalaj · 0 citations