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In this paper, we discuss the minimal surfaces over the slanted half-planes, vertical strips, and single slit whose slit lies on the negative real axis. The representation of these minimal surfaces and the corresponding harmonic mappings are obtained explicitly. Finally, we illustrate the harmonic mappings of each of these cases together with their minimal surfaces pictorially with the help of mathematica.
We investigate the existence of non-trivial holomorphic and meromorphic solutions of Fermat functional equations over an open Riemann surface $S$. When $S$ is hyperbolic, we prove that any $k$-term Fermat functional equation always exists non-trivial
The determination of the density matrix of an ensemble of identically prepared quantum systems by performing a series of measurements, known as quantum tomography, is minimal when the number of outcomes is minimal. The most accurate minimal quantum t
We prove a version of the strong half-space theorem between the classes of recurrent minimal surfaces and complete minimal surfaces with bounded curvature of $mathbb{R}^{3}_{raisepunct{.}}$ We also show that any minimal hypersurface immersed with bou
Normalized exponential sums are entire functions of the form $$ f(z)=1+H_1e^{w_1z}+cdots+H_ne^{w_nz}, $$ where $H_1,ldots, H_ninC$ and $0<w_1<ldots<w_n$. It is known that the zeros of such functions are in finitely many vertical strips $S$. The
The $Pi$-operator, also known as Ahlfors-Beurling transform, plays an important role in solving the existence of locally quasiconformal solutions of Beltrami equations. In this paper, we first construct the $Pi$-operator on a general Clifford-Hilbert