Harmonic functions starlike of the complex order
Harmonic mappings in the exterior of the unit disk
In this paper we consider a class of univalent orientation-preserving harmonic functions defined on the exterior of the unit disk which satisfy the condition [...] . We are interested in finding radius of univalence and convexity for such class and we find extremal functions. Convolution, convex combination, and explicit quasiconformal extension for this class are also determined.
Harmonic mappings onto parallel slit domains
We consider typically real harmonic univalent functions in the unit disk 𝔻 whose range is the complex plane slit along infinite intervals on each of the lines x ± ib, b > 0. They are obtained via the shear construction of conformal mappings of 𝔻 onto the plane without two or four half-lines symmetric with respect to the real axis.
Harmonic maps from surfaces to certain Kaehler manifolds.
Harmonic parametrization of geodesic quadrangles on surfaces of constant curvature and 2-D quasi-isometric grids.
Harmonic starlike functions of complex order involving hypergeometric functions
Harmonic univalent functions defined by an integral operator.
Hausdorff convergence and the limit shape of the unicorns.
Hausdorff dimension and quasisymmetric mappings.
Hausdorff dimension of harmonic measure on the boundary of an attractive basin for a holomorphic map.
Hausdorff dimension of quasi-circles
Hausdorff measure of the singular set of quasiregular maps on Carnot groups.
Heating of the Beurling operator: Sufficient conditions for the two-weight case
We establish sufficient conditions on the two weights w and v so that the Beurling-Ahlfors transform acts continuously from to L²(v). Our conditions are simple estimates involving heat extensions and Green’s potentials of the weights.
Hebbare Singularitäten quasikonformer Abbildungen und lokal beschränkter holomorpher Funktionen.
Heights of powers of Newman and Littlewood polynomials
Hencky-Prandtl nets and constant principal strain mappings with isolated singularities.
Hénon mappings in the complex domain I : the global topology of dynamical space
Hermite interpolation and an inequality for entire functions of exponential type.
Hermitean Cauchy integral decomposition of continuous functions on hypersurfaces.
Hermitian composition operators on Hardy-Smirnov spaces
Let Ω be an open simply connected proper subset of the complex plane and φ an analytic self map of Ω. If f is in the Hardy-Smirnov space defined on Ω, then the operator that takes f to f ⃘ φ is a composition operator. We show that for any Ω, analytic self maps that induce bounded Hermitian composition operators are of the form Φ(w) = aw + b where a is a real number. For ceratin Ω, we completely describe values of a and b that induce bounded Hermitian composition operators.