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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

An example of a harmonic map between Euclidean balls


Author: Antonios D. Melas
Journal: Proc. Amer. Math. Soc. 117 (1993), 857-859
MSC: Primary 58E20
MathSciNet review: 1112497
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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 [Enhancements On Off] (What's this?)

  • [C] 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 0016973 (8,93a)
  • [K] H. Kneser, Lösung der Aubgabe $ 41$, Jber. Deutsch. Math.-Verein. 35 (1926), 123-124.
  • [R] T. Radó, Augabe $ 41$, Jber. Deutsch. Math.-Verein. 35 (1926), 49.

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1993-1112497-9
PII: S 0002-9939(1993)1112497-9
Article copyright: © Copyright 1993 American Mathematical Society