We study harmonic maps between surfaces, that are solutions to a nonlinear elliptic PDE. In Refs. Minsky (1992); Wolf (1989) it was proved diffeomorphisms, with nonvanishing Hopf differential, satisfy Beltrami equation of certain type: the imaginary part logarithm coefficient coincides differential. Therefore, is function. The real satisfies an differential equation, which in case constant curv...

in this paper, we focus on the study of shearlet transform which isdened by using the hyperbolic functions. as a result we check an admissibilitycondition such that implies the reconstruction formula. to this end, we will usethe concept of the classical shearlet, which indicates the position and directionof a singularity.

Elliptic and hyperbolic cylindrical curves satisfying Tzitzeica condition are obtained via the solution of the forced harmonic equation. Mathematics Subject Classification: 53A04, 34A05.

In this paper we give a method for constructing complex valued harmonic morphisms in some pseudo-Riemannian manifolds using a parametrization of isotropic subbundles of the complexified tangent bundle. As a result we construct the first known examples of complex valued harmonic morphisms in real hyperbolic spaces of even dimension not equal to 4 which do not have totally geodesic fibres.

We prove that a positive function on the unit disk admits a harmonic majorant if and only if a certain explicit upper envelope of it admits a superharmonic majorant. We provide examples to show that mere superharmonicity of the data does not help with the problem of existence of a harmonic majorant. 1. Definitions and statements Let D stand for the open unit disk in the complex plane, and H(D) ...

We describe the relationship between complex-valued harmonic morphisms from Minkowski 4-space and the shear-free ray congruences of mathematical physics. Then we show how a horizontally conformal submersion on a domain of R 3 gives the boundary values at infinity of a complex-valued harmonic morphism on hyperbolic 4-space.

Abstract Using harmonic mean curvature flow, we establish a sharp Minkowski-type lower bound for total of convex surfaces with given area in Cartan-Hadamard $3$-manifolds. This inequality also improves the known estimates hyperbolic $3$-space. As an application, obtain Bonnesen-style isoperimetric distance function nonpositively curved $3$-spaces, via monotonicity results curvature. connection ...

We present a computational approach for the WKB approximation of the wave function of an electron moving in a periodic one-dimensional crystal lattice by means of a nonstrictly hyperbolic system whose flux function stems from the Bloch spectrum of the Schrödinger operator. This second part focuses on the handling of the source terms which originate from slowly-varying exterior potentials. Physi...

‎In this paper we characterize Bergman spaces with‎ ‎respect to double integral of the functions $|f(z)‎ ‎-f(w)|/|z-w|$,‎ ‎$|f(z)‎ -‎f(w)|/rho(z,w)$ and $|f(z)‎ ‎-f(w)|/beta(z,w)$,‎ ‎where $rho$ and $beta$ are the pseudo-hyperbolic and hyperbolic metrics‎. ‎We prove some necessary and sufficient conditions that implies a function to be...