Jordan domains with a rectifiable arc in their boundary

2017/05/05 by Vasiliki Liontou, Liontou, V., Vassili Nestoridis +1
Mathematics · #30H10 #Algebraic and Geometric Analysis #Analytic and geometric function theory #Classical Analysis and ODEs (math.CA) #Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.1705.02254

openalex publication_date 2017/05/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that if an open arc J of the boundary of a Jordan domain Ω is rectifiable, then the derivative Φ' of the Riemann map Φ: D→ Ω from the open unit disk D onto Ω behaves as an H¹ function when we approach the arc Φ^-1(J^′),where J^′ is any compact subarc of J. "

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