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The global homeomorphism theorem for space quasiconformal mappings, its development and related open problems

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Quasiconformal Space Mappings

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1508))

Abstract

The global homeomorphism theorem is the following specifically multidimensional phenomenon: any locally homeomorphic quasiconformal mapping f: R n → R n is a bijection if n≥3.

We present here a brief review of results and open problems related to this theorem.

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  1. Moscow University, 119899, Moscow, Russia

    V. A. Zorich

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Matti Vuorinen

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Dedicated to Gerhard and Inge Krautschneider

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Zorich, V.A. (1992). The global homeomorphism theorem for space quasiconformal mappings, its development and related open problems. In: Vuorinen, M. (eds) Quasiconformal Space Mappings. Lecture Notes in Mathematics, vol 1508. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0094243

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  • DOI: https://doi.org/10.1007/BFb0094243

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