Bieberbach conjecture, Bohr radius, Bloch constant and Alexander's theorem in infinite dimensions
Year: 2024
Type: preprint
Abstract: In this paper, we investigate holomorphic mappings $F$ on the unit ball $\mathbb{B}$ of a complex Banach space of the form $F(x)=f(x)x$, where $f$ is a holomorphic function on $\mathbb{B}$. First, we investigate criteria for univalence, starlikeness and quasi-convexity of type $B$ on $\mathbb{B}$. Next, we investigate a generalized Bieberbach conjecture, a covering theorem and a distortion theorem, the Fekete-Szegö inequality, lower bound for the Bloch constant, and Alexander's type theorem for such mappings.
Source: arXiv (Cornell University)
Authors: Hamada, Hidetaka, Kohr, Gabriela, Kohr, Mirela
Institution: Babeș-Bolyai University
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4403586139