Jordan domains with a rectifiable arc in their boundary

V. Liontou; V. Nestoridis

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arXiv · 1705.02254

Jordan domains with a rectifiable arc in their boundary

V. Liontou·V. Nestoridis

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Abstract

We show that if an open arc J of the boundary of a Jordan domain $\Omega$ is rectifiable, then the derivative $\Phi$' of the Riemann map $\Phi: D\rightarrow \Omega$ from the open unit disk D onto $\Omega$ behaves as an $H^1$ function when we approach the arc $\Phi^{-1}(J^{\prime})$,where $J^{\prime}$ is any compact subarc of $J$. "

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V. Liontou, V. Nestoridis. 2017-05-05. Jordan domains with a rectifiable arc in their boundary. https://arxiv.org/abs/1705.02254

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