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.

An explicit fully discrete finite element method, which satisfies the nonconvex side constraint at every node, is developed for approximating the p-harmonic flow for p ∈ (1,∞). Convergence of the method is established under certain conditions on the domain and mesh. Computational examples are presented to demonstrate finite-time blow-ups and qualitative geometric changes of weak solutions of th...

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.

We prove that at a finite singular time for the Harmonic Ricci Flow on a surface of positive genus both the energy density of the map component and the curvature of the domain manifold have to blow up simultaneously. As an immediate consequence, we obtain smooth long-time existence for the Harmonic Ricci Flow with large coupling constant.

We consider harmonic functions with respect to the operator Lu(x) = ∫ [u(x+ h)− u(x)− 1(|h|≤1)h · ∇u(x)]n(x, h) dh. Under suitable conditions on n(x, h) we establish a Harnack inequality for functions that are nonnegative and harmonic in a domain. The operator L is allowed to be anisotropic and of variable order.

We investigate the relationship between the univalence of f and of h in the decomposition f = h+g of a sense-preserving harmonic mapping defined in the unit disk D ⊂ C. Among other results, we determine the holomorphic univalent maps h for which there exists c > 0 such that every harmonic mapping of the form f = h + g with |g| < c|h| is univalent. The notion of a linearly connected domain appea...

A new fictitious domain model for topology optimization of time-harmonic problems based on a wave to diffusion equation transition is proposed. By employing negative values appropriate material coefficients, tuneable exponential decay the field amplitude in domains can be obtained, whereas conventional finite always present. To demonstrate applicability model, we consider two problems; volume m...

Cλ-extended oscillator algebras are realized as generalized deformed oscillator algebras. For λ = 3, the spectrum of the corresponding bosonic oscillator Hamiltonian is shown to strongly depend on the algebra parameters. A connection with cyclic shape invariant potentials is noted. A bosonization of PSSQM of order two is obtained. PACS: 03.65.Fd