Abstract
It is shown that every one-to-one pluriharmonic mapping of a neighborhood of 0ε R4 into itself has nonvanishing Jacobian.
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H. Lewy, “On the nonvanishing of the Jacobian for certain one-to-one mappings,” Uspekhi Mat. Nauk,3, No. 2, 216–219 (1948).
H. Lewy, “On the nonvanishing of the Jacobian of a homeomorphism by harmonic gradients,” Ann. Math., Ser. 2,88, No. 3, 518–629 (1968).
B. A. Fuks, Theory of Analytic Functions of Several Complex Variables, American Mathematics (1965).
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Translated from Matematicheskii Zametki, Vol. 13, No. 2, pp. 189–194, February, 1973.
In conclusion, the author wishes to thank B. V. Shabat and E. M. Chirka for their help with this work.
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Naser, M. A generalization of a theorem of Lewy on harmonic mappings. Mathematical Notes of the Academy of Sciences of the USSR 13, 113–115 (1973). https://doi.org/10.1007/BF01094227
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DOI: https://doi.org/10.1007/BF01094227