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We show that there exist planar Jordan domains $\Omega_1$ and $\Omega_2$ with boundaries of Hausdorff dimension $1$ such that any conformal maps $\varphi_1 \colon \mathbb D \to \Omega_1$ and $\varphi_2… Click to show full abstract
We show that there exist planar Jordan domains $\Omega_1$ and $\Omega_2$ with boundaries of Hausdorff dimension $1$ such that any conformal maps $\varphi_1 \colon \mathbb D \to \Omega_1$ and $\varphi_2 \colon \Omega_2 \to \mathbb D $ cannot be extended as global homeomorphisms between the Riemann spheres of $W^{1,\,1}$ class (or even not in $BV$).
Keywords:
conformal boundary;
boundary values;
schoenflies solutions;
solutions conformal;
may fail;
values may
Journal Title: Annales Academiae Scientiarum Fennicae Mathematica
Year Published: 2019
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Journal Title: Annales Academiae Scientiarum Fennicae Mathematica
Year Published: 2019
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!