Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 38, 2013, 327-340

ANOTHER PROOF OF THE LIOUVILLE THEOREM

Zhuomin Liu

University of Pittsburgh, Department of Mathematics
301 Thackeray Hall, Pittsburgh, PA 15260, U.S.A.; zhl26 'at' pitt.edu

Abstract. We provide another proof of the Liouville theorem that conformal mappings in the dimensions at least three are Möbius transformations under the assumption that the mapping is 1-quasiconformal. Our method employs the Ahlfors Cauchy-Riemann operator.

2010 Mathematics Subject Classification: Primary 35B53, 30C35, 30C65; Secondary 46E35.

Key words: The Liouville theorem, 1-quasiconformal mappings.

Reference to this article: Z. Liu: Another proof of the Liouville theorem. Ann. Acad. Sci. Fenn. Math. 38 (2013), 327-340.

Full document as PDF file

doi:10.5186/aasfm.2013.3807

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