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Boundary geometry and linear accessibility of functions with positive real derivative

  • Shota Hoshinaga
  • Ikkei Hotta
  • Li-Mei Wang
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Abstract

We study the boundary geometry of the Noshiro--Warschawski class ℛ. Using the geometric structure of close-to-convex domains and their relation to Loewner chains, we investigate the boundary behavior of functions in 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 ℛ need not be locally connected. We also revisit the classical fact that ℛ is not contained in the class 𝒮* of starlike functions and give a simple explicit example of a function in ℛ∖𝒮*.

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Cite

BibTeXRIS
BibTeX
@misc{hoshinaga2026boundary,
  title = {{Boundary geometry and linear accessibility of functions with positive real derivative}},
  author = {Shota Hoshinaga and Ikkei Hotta and Li-Mei Wang},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.20988},
  eprint = {2609.20988},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.20988},
}
RIS
TY  - UNPB
TI  - Boundary geometry and linear accessibility of functions with positive real derivative
AU  - Shota Hoshinaga
AU  - Ikkei Hotta
AU  - Li-Mei Wang
PY  - 2026
DA  - 2026/09/17
PB  - arXiv
DO  - 10.48550/arxiv.2609.20988
UR  - https://arxiv.org/abs/2609.20988
AB  - We study the boundary geometry of the Noshiro--Warschawski class ℛ. Using the geometric structure of close-to-convex domains and their relation to Loewner chains, we investigate the boundary behavior of functions in 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 ℛ need not be locally connected. We also revisit the classical fact that ℛ is not contained in the class 𝒮^* of starlike functions and give a simple explicit example of a function in ℛ∖𝒮^*.
ER  -