We show that each Jordan homomorphism R→ R′ of rings gives rise to a harmonic mapping of one connected component of the projective line over R into the projective line over R′. If there is more than one connected component then this mapping can be extended in various ways to a harmonic mapping which is defined on the entire projective line over R. Mathematics Subject Classification (2000): 51C0...

Given two univalent harmonic mappings f1 and f2 on D, which lift to minimal surfaces via the Weierstrass-Enneper representation theorem, we give necessary and sufficient conditions for f3 = (1−s)f1+sf2 to lift to a minimal surface for s ∈ [0, 1]. We then construct such mappings from Enneper’s surface to Scherk’s singularly periodic surface, Sckerk’s doubly periodic surface to the catenoid, and ...

We present an efficient adaptive method to compute the harmonic volumetric mapping, which establishes a smooth correspondence between two given solid objects of the same topology. We solve a sequence of charge systems based on the harmonic function theory and the method of fundamental solutions (MFS) for designing the map with boundary and feature constraints. Compared to the previous harmonic ...

In [11] the author proved that every quasiconformal harmonic mapping between two Jordan domains with C, 0 < α ≤ 1, boundary is biLipschitz, providing that the domain is convex. In this paper we avoid the restriction of convexity. More precisely we prove: any quasiconformal harmonic mapping between two Jordan domains Ωj , j = 1, 2, with C, j = 1, 2 boundary is bi-Lipschitz.

We developed two techniques to address 3D volume parameterization and deformation mapping problems that arise in medical imaging [1]. The first algorithm finds a harmonic map from a 3-manifold to a 3D solid sphere and the second is a novel sphere carving algorithm which calculates the simplicial decomposition of a complex 3D image volume while preserving its surface topology. In this paper, we ...

Second-harmonic generation microscopy (SHGM) has been employed to study crystals of zeolite-like material SAPO-5 filled with p-nitroaniline (PNA). The SHG and 2-photon fluorescence response of PNA in the one-dimensional channels readily reveals the pore accessibility; intergrown crystallites containing hexagonal pyramidal components and internal diffusion barriers are found next to seemingly pe...

Recommended by Narendra Kumar Govil We first obtain the relations of local univalency, convexity, and linear connectedness between analytic functions and their corresponding affine harmonic mappings. In addition, the paper deals with the regions of variability of values of affine harmonic and biharmonic mappings. The regions their boundaries are determined explicitly and the proofs rely on Schw...

This paper describes an approach of representing 3D shape by using a set of invariant Spherical Harmonic (SH) coefficients after conformal mapping. Specifically, a genus-zero 3D mesh object is first conformally mapped onto the unit sphere by using a modified discrete conformal mapping, where the modification is based on Möbius Factorization and is aimed at obtaining a canonical conformal mappin...

It is shown that an analytic function taking circles to ellipses must be a Möbius transformation. It then follows that a harmonic mapping taking circles to ellipses is a harmonic Möbius transformation. Analytic Möbius transformations take circles to circles. This is their most basic, most celebrated geometric property. We add the adjective ‘analytic’ because in a previous paper [1] we introduce...