Capacity densities and angular limits of quasiregular mappings
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- by Matti Vuorinen
- Trans. Amer. Math. Soc. 263 (1981), 343-354
- DOI: https://doi.org/10.1090/S0002-9947-1981-0594412-6
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Abstract:
It is shown that if a bounded quasiregular mapping of the unit ball ${B^n} \subset {R^n}$, $n \geqslant 2$, has a limit at $b \in \partial {B^n}$ through a set $E \subset {B^n}$ with $b \in \bar E$, then it has an angular limit at $b$ provided that $E$ is contained in an open cone $C \subset {B^n}$ with vertex $b$ and that $E$ is thick enough at $b$. The thickness condition is expressed in terms of the $n$-capacity density.References
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Bibliographic Information
- © Copyright 1981 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 263 (1981), 343-354
- MSC: Primary 30C60
- DOI: https://doi.org/10.1090/S0002-9947-1981-0594412-6
- MathSciNet review: 594412