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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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An example of a harmonic map between Euclidean balls
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by Antonios D. Melas PDF
Proc. Amer. Math. Soc. 117 (1993), 857-859 Request permission

Abstract:

Here we construct a homeomorphism of the unit sphere in three-dimensional Euclidean space to itself whose harmonic extension in the unit ball is not a diffeomorphism.
References
  • Gustave Choquet, Sur un type de transformation analytique généralisant la représentation conforme et définie au moyen de fonctions harmoniques, Bull. Sci. Math. (2) 69 (1945), 156–165 (French). MR 16973
    • H. Kneser, Lösung der Aubgabe $41$, Jber. Deutsch. Math.-Verein. 35 (1926), 123-124. T. Radó, Augabe $41$, Jber. Deutsch. Math.-Verein. 35 (1926), 49.
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Additional Information
  • © Copyright 1993 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 117 (1993), 857-859
  • MSC: Primary 58E20
  • DOI: https://doi.org/10.1090/S0002-9939-1993-1112497-9
  • MathSciNet review: 1112497