We study the extremal problem for weighted combined energy between two concentric
annuli and obtain that the extremal mapping is a certain radial mapping. This extends the …

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 …

We consider the so called combined energy of a deformation between two concentric annuli
and minimize it, provided that it keep order of the boundaries. It is an extension of the …

We study hereditary properties of convexity for planar harmonic homeomorphisms on a disk
and an annulus. A noteworthy class of examples with the hereditary property arises from …

We extend the celebrated theorem of Kellogg for conformal mappings to the minimizers of
Dirichlet energy. Namely we prove that a diffeomorphic minimizer of Dirichlet energy of …

In this paper, we consider minimal graphs in the three-dimensional Riemannian manifold
M× R. We mainly estimate the Gaussian curvature of such surfaces. We consider the …

HEREDITARY CIRCULARITY FOR ENERGY MINIMAL DIFFEOMORPHISMS 1. Introduction
Harmonic mappings between planar regions are generaliz Page 1 CONFORMAL GEOMETRY …

We extend the main results obtained by Iwaniec and Onninen in Memoirs of the AMS (2012).
In this paper, we solve the (ρ, n)(ρ, n)-energy minimization problem for Sobolev …

We consider the existence and uniqueness of a minimizer of the extremal problem for
weighted combined energy between two concentric annuli and obtain that the extremal …

We study a hereditary starlikeness property for planar harmonic mappings on a disk and on
an annulus. While such a property is a common trait of conformal mappings, it may be …