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Characterizations of φ-inner uniform domains and φ-uniform domains in metric spaces

  • Shu-Jing Gao
  • Miao He
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Abstract

In this paper, we study φ-uniform/-inner uniform domains in metric spaces. In our first main result, we establish quantitative characterizations of three different definitions of φ-uniformity/-inner uniformity in length spaces. In our second main result, we obtain a geometric sufficient condition of φ-uniform/-inner uniform domains in doubling length spaces, which extends the corresponding result of Guo-Huang-Wang [arXiv 2025] and Gao-Guo-Huang-Wang [arXiv 2025] for linear case.

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Cite

BibTeXRIS
BibTeX
@misc{gao2026characterizations,
  title = {{Characterizations of $φ$-inner uniform domains and $φ$-uniform domains in metric spaces}},
  author = {Shu-Jing Gao and Miao He},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.39574},
  eprint = {2610.39574},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.39574},
}
RIS
TY  - UNPB
TI  - Characterizations of φ-inner uniform domains and φ-uniform domains in metric spaces
AU  - Shu-Jing Gao
AU  - Miao He
PY  - 2026
DA  - 2026/10/29
PB  - arXiv
DO  - 10.48550/arxiv.2610.39574
UR  - https://arxiv.org/abs/2610.39574
AB  - In this paper, we study φ-uniform/-inner uniform domains in metric spaces. In our first main result, we establish quantitative characterizations of three different definitions of φ-uniformity/-inner uniformity in length spaces. In our second main result, we obtain a geometric sufficient condition of φ-uniform/-inner uniform domains in doubling length spaces, which extends the corresponding result of Guo-Huang-Wang [arXiv 2025] and Gao-Guo-Huang-Wang [arXiv 2025] for linear case.
ER  -