Picard's theorem and Rickman's theorem by way of Harnack's inequality

Author:
John L. Lewis

Journal:
Proc. Amer. Math. Soc. **122** (1994), 199-206

MSC:
Primary 30C65

DOI:
https://doi.org/10.1090/S0002-9939-1994-1195483-3

MathSciNet review:
1195483

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Abstract: In this note we give a very elementary proof of Picard's Theorem and Rickman's Theorem which uses only Harnack's inequality.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1994-1195483-3

Keywords:
Picard's theorem,
harmonic functions,
Harnack's inequality,
quasiregular mappings,
omitted values,
unique continuation

Article copyright:
© Copyright 1994
American Mathematical Society