Harmonic close-to-convex functions and minimal surfaces

Harmonic Close-to-convex Mappings

Sufficient coefficient conditions for complex functions to be close-to-convex harmonic or convex harmonic are given. Construction of close-to-convex harmonic functions is also studied by looking at transforms of convex analytic functions. Finally, a convolution property for harmonic functions is discussed. Harmonic, Convex, Close-to-Convex, Univalent.

Some Properties of Certain Subclasses of Close-to-Convex and Quasi-convex Functions with Respect to 2k-Symmetric Conjugate Points

Minimal Surfaces and Harmonic Functions in the Heisenberg Group

We study the blow-up of H-perimeter minimizing sets in the Heisenberg group H, n ≥ 2. We show that the Lipschitz approximations rescaled by the square root of excess converge to a limit function. Assuming a stronger notion of local minimality, we prove that this limit function is harmonic for the Kohn Laplacian in a lower dimensional Heisenberg group.

An Investigation on Minimal Surfaces of Multivalent Harmonic Functions

The projection on the base plane of a regular minimal surface S in R with isothermal parameters defines a complex-valued univalent harmonic function f = h(z) + g(z). The aim of this paper is to obtain the distortion inequalities for the Weierstrass-Enneper parameters of the minimal surface for the harmonic multivalent functions for which analytic part is an m-valent convex function. 2000 Mathem...

some properties of certain subclasses of close-to-convex and quasi-convex functions with respect to 2k-symmetric conjugate points

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