We determine the extremal mappings with smallest mean distortion for mappings of annuli.
As a corollary, we find that the Nitsche harmonic maps are Dirichlet energy minimizers …

The central theme of this paper is the variational analysis of homeomorphisms $
h\colon\mathbb X\xrightarrow []{{} _ {\!\!\mathrm {onto}\!\!}}\mathbb Y $ between two given …

The Nitsche conjecture is deeply rooted in the theory of doubly-connected minimal surfaces.
However, it is commonly formulated in slightly greater generality as a question of existence …

Let and be two circular annuli and let be a radial metric defined in the annulus. Consider the
class of-harmonic mappings between and. It is proved recently by Iwaniec, Kovalev and …

Let ρ Σ= h (| z| 2) be a metric in a Riemann surface Σ, where h is a positive real function. Let
H r 1={w= f (z)} be the family of a univalent ρ Σ harmonic mapping of the Euclidean annulus …

The paper is concerned with mappings h : X between planar domains having least Dirichlet
energy. The existence and uniqueness (up to a conformal change of variables in X) of the …

Abstract Let X={x ∈ R^ 2; r<| x|< R\} and Y={y ∈ R^ 2; r_ ∗<| y|< R_ ∗\} be annuli in the
plane. We consider the class F (X, Y) of all orientation preserving homeomorphisms h: X …

Abstract Let A and A∗ be circular annuli in the complex plane, and consider the Dirichlet
energy integral of j-degree mappings between A and A∗. We aim to minimize this energy …

The concept of a conformal deformation has two natural extensions: quasiconformal and
harmonic mappings. Both classes do not preserve the conformal type of the domain …

Let ρ ρ be a radial symmetric Riemannian metric defined in the annulus A (1, R). Kalaj
conjectured that if there exists a ρ ρ-harmonic homeomorphism from the annulus A (1, r) …