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math.CV2026
A Jacobian Group Structure on a Hyperbolic Pencil of circles and its Applications
Faruk F. Abi-Khuzam
Using Jacobian Elliptic functions, we introduce a novel parametrization of a hyperbolic pencil of coaxal circles which reveals a remarkable group structure on the pencil. The geome…
math.CV2022
Dimension Free Growth Results for Vector-Valued Functions of Several Complex Variables
Faruk F. Abi-Khuzam
Let f be an entire function of finite order less than 1. The maximum modulus M(r) of f and the counting function of the zeros N(r) are connected by a best possible growth inequalit…
math.CV2017
The star function for meromorphic functions of several complex variables
Faruk Abi-Khuzam, Florian Bertrand, Giuseppe Della Sala
We define an analogue of the Baernstein star function for a meromorphic function f in several complex variables. This function is subharmonic on the upper half-plane and encodes so…