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Convolutions of harmonic right half-plane mappings

100%

Li Y., Liu Z.

Open Mathematics

2016

tom 14

nr 1

789-800

We first prove that the convolution of a normalized right half-plane mapping with another subclass of normalized right half-plane mappings with the dilatation [...] −z(a+z)/(1+az) $ - z(a + z)/(1 + az)$ is CHD (convex in the horizontal direction) provided [...] a=1 $a = 1$ or [...] −1≤a≤0 $ - 1 \le a \le 0$ . Secondly, we give a simply method to prove the convolution of two special subclasses of harmonic univalent mappings in the right half-plane is CHD which was proved by Kumar et al. [1, Theorem 2.2]. In addition, we derive the convolution of harmonic univalent mappings involving the generalized harmonic right half-plane mappings is CHD. Finally, we present two examples of harmonic mappings to illuminate our main results.

Harmonicity of vector fields on four-dimensional generalized symmetric spaces

64%

Calvaruso G.

Open Mathematics

2012

tom 10

nr 2

411-425

Let (M = G/H;g)denote a four-dimensional pseudo-Riemannian generalized symmetric space and g = m + h the corresponding decomposition of the Lie algebra g of G. We completely determine the harmonicity properties of vector fields belonging to m. In some cases, all these vector fields are critical points for the energy functional restricted to vector fields. Vector fields defining harmonic maps are also classified, and the energy of these vector fields is explicitly calculated.

Ograniczanie wyników

2 Open Mathematics

1 Calvaruso G.

1 Li Y.

1 Liu Z.

1 2016

1 2012

Wyniki wyszukiwania

Convolutions of harmonic right half-plane mappings

Harmonicity of vector fields on four-dimensional generalized symmetric spaces