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arXiv · 1709.07324

Beltrami system and 1-quasiconformal embeddings in higher dimensions

Tao Cheng·Huanhuan Yang·Shanshuang Yang
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Abstract

In this paper we derive necessary and sufficient conditions for a smooth surface in Rn+1 to admit a local 1-quasiconformal parameterization by a domain in Rn (n >= 3). We then apply these conditions to specific hypersurfaces such as cylinders, paraboloids, and ellipsoids. As a consequence, we show that the classical Liouville theorem about the rigidity of 1-quasiconformal maps between domains in Rn with n >= 3 does not extend to embeddings of domains into a higher dimensional space.

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Tao Cheng, Huanhuan Yang, Shanshuang Yang. 2017-09-21. Beltrami system and 1-quasiconformal embeddings in higher dimensions. https://arxiv.org/abs/1709.07324

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