Year: 2026
Type: preprint
Abstract: We study the boundary geometry of the Noshiro--Warschawski class $\mathcal{R}$. Using the geometric structure of close-to-convex domains and their relation to Loewner chains, we investigate the boundary behavior of functions in $\mathcal{R}$. In particular, we discuss the relation between spherical length and local connectedness, and show that the boundary of the image domain of a function in $\mathcal{R}$ need not be locally connected. We also revisit the classical fact that $\mathcal{R}$ is not contained in the class $\mathcal{S}^{*}$ of starlike functions and give a simple explicit example of a function in $\mathcal{R}\setminus\mathcal{S}^*$.
Source: arXiv (Cornell University)
Authors: Hoshinaga, Shota, Hotta, Ikkei, Wang, Li-Mei
Institution: National Institute of Technology, Kure College
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7213890441