7 papers · 1 filter
On an Iwaniec--Kovalev--Onninen Conjecture for harmonic quasiconformal annulus mappings
David Kalaj, Jinsong Liu, Jian-feng Zhu
In 2012, Iwaniec, Kovalev and Onninen proposed an upper Nitsche--Grötzsch type estimate for harmonic -quasiconformal homeomorphisms between circular annuli: in normalized form,…
Bergman barycentric extensions of boundary homeomorphisms of the complex ball
David Kalaj, Anton Gjokaj, Vladimir Jacimovic
We define a Bergman barycentric extension of boundary homeomorphisms of the complex unit ball by \[ E_B(f)(z)=\barB(f_*σ_z), \] where \(\barB\) is the Busemann barycenter for the B…
A Lewy-type theorem for pluriharmonic mappings in $\C^2$ and bi-Lipschitz quasiconformal harmonic maps
David Kalaj
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 ho…
The Gromov--Ros conjecture for rank-one symmetric spaces of noncompact type
David Kalaj
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 is…
A Lewy theorem for harmonic quasiregular mappings in three-space
David Kalaj, Jian-Feng Zhu
Lewy's classical theorem asserts that a one-to-one planar harmonic mapping has nonvanishing Jacobian. We prove a three-dimensional bounded-distortion analogue: if \[ f:Ω\subset \ma…
The Nitsche--Hopf conjecture for minimal graphs
David Kalaj, Jian-Feng Zhu
We prove the Nitsche--Hopf conjecture for non-parametric minimal graphs over disks. If \(S\) is a minimal graph over a disk of radius \(R\), and if \(ξ\) is the point above the cen…
On an extremal problem for harmonic maps conformal at a point
Franc Forstneric, David Kalaj
Let \(\mathbb D\) denote the unit disc in \(\mathbb C\). For a domain \(D\subset\mathbb C\) and a point \(p\in D\), let \(M_D(p)\) denote the supremum of \(\|df_0\|\) over all harm…