Related papers: Linear measure and $K$-quasiconformal harmonic map…
Using only linear interactions and a local parity measurement we show how entanglement can be detected between two harmonic oscillators. The scheme generalizes to measure both linear and non-linear functionals of an arbitrary oscillator…
In this article we introduce a natural extension of the well-studied equation for harmonic maps between Riemannian manifolds by assuming that the target manifold is equipped with a connection that is metric but has non-vanishing torsion.…
We first construct the harmonic K-quasiconformal Koebe functions, filling a long-standing foundational gap in geometric function theory. This construction provides a unified parametric candidate extremal function framework for conformal…
In this short survey we report on the theory of biharmonic maps between Riemannian manifolds.
We investigate integral-geometric quantities arising from harmonic analysis which measure visibility and transversality. Motivated by their applications in multilinear Kakeya problems and affine-invariant measures on surfaces, we derive…
We investigate some properties of balayage, or, sweeping (out), of measures with respect to subclasses of subharmonic functions. The following issues are considered: relationships between balayage of measures with respect to classes of…
In this paper, we first establish the Schwarz-Pick lemma of higher-order and apply it to obtain a univalency criteria for planar harmonic mappings. Then we discuss distortion theorems, Lipschitz continuity and univalency of planar harmonic…
The purpose of this paper is to study the harmonicity of maps to or from para-Sasakian manifolds. We derive the condition for the tension field of paraholomorphic map between almost para-Hermitian manifold and para-Sasakian manifold. The…
In this paper, we investigate the properties of locally univalent and multivalent planar harmonic mappings. First, we discuss the coefficient estimates and Landau's Theorem for some classes of locally univalent harmonic mappings, and then…
In the paper, we study variation formulas for transversally harmonic maps and bi-harmonic maps, respectively. We also study the transversal Jacobi field along a map and give several relations with infinitesimal automorphisms.
Conic quasi-linear maps are nonlinear operators from $C_0(X)$ to a normed linear space $E$ which preserve nonnegative linear combinations on positive cones generated by single functions; quasi-linear maps are linear on singly generated…
We study the Dirichlet problem for harmonic maps between hyperbolic planes, under the assumption that the Euclidean harmonic extension of the boundary map is quasiconformal.
In this brief survey we give an introduction to some aspects of "atoms" on metric spaces and their connection with linear operators.
This paper contains bounds for the distortion in the spherical metric, that is to say bounds for the constant of Holder continuity of mappings f : (\Rn,q) -> (\Rn, q) where q denotes the spherical metric. The mappings considered are…
Nonlinearity in many systems is heavily dependent on component variation and environmental factors such as temperature. This is often overcome by keeping signals close enough to the device's operating point that it appears approximately…
Linear noise-reduction filters used in spectroscopy must strike a balance between reducing noise and preserving lineshapes, the two conflicting requirements of interest.
This note reviews some of the recent work on biharmonic conformal maps (see \cite{OC}, Chapter 11, for a detailed survey). It will be focused on biharmonic conformal immersions and biharmonic conformal maps between manifolds of the same…
On foliations, there are two kinds of harmonic maps, that is, transversally harmonic map and $(F,F')$-harmonic map which are equivalent when the foliation is minimal. In this paper, we study transversally f-harmonic and $(F,F')_f$-harmonic…
In this paper, we define both the upper and lower order of a sense-preserving harmonic mapping in $\mathbb{D}$. We generalize to the harmonic case some known results about holomorphic functions with positive lower order and we show some…
The measurement of a quantum system becomes itself a quantum-mechanical process once the apparatus is internalized. That shift of perspective may result in different physical predictions for a variety of reasons. We present a model…