2023年3月
BMO embeddings, chord-arc curves, and Riemann mapping parametrization
Advances in Mathematics
- ,
- 巻
- 417
- 号
- 記述言語
- 英語
- 掲載種別
- 研究論文(学術雑誌)
- DOI
- 10.1016/j.aim.2023.108933
We consider the space of chord-arc curves on the plane passing through infinity with their parametrization γ defined on the real line, and embed this space into the product of the BMO Teichmüller spaces. The fundamental theorem we prove about this representation is that γ↦logγ′ is a biholomorphic homeomorphism into the complex Banach space of BMO functions. Using these two equivalent complex structures, we develop a clear exposition on the analytic dependence of involved mappings between certain subspaces. Especially, we examine the parametrization of a chord-arc curve by using the Riemann mapping and its dependence on the arc-length parametrization. As a consequence, we can solve the conjecture of Katznelson, Nag, and Sullivan by showing that this dependence is not continuous.
- リンク情報
- ID情報
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- DOI : 10.1016/j.aim.2023.108933
- ISSN : 0001-8708
- eISSN : 1090-2082
- SCOPUS ID : 85149867539