关于Martio猜想的注记

Pub Date : 2020-06-26 DOI:10.7146/math.scand.a-132257

Ville Tengvall

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引用次数: 2

摘要

我们引入了Jacobian行列式倒数的一个可积条件，它保证了具有小内扩张的拟正则映射的局部同胚性。在平面情况下，这种情况是尖锐的。我们还证明了具有小内扩张的拟正则映射的每个分支点都是该映射的微分矩阵的Lebesgue点。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Remarks on Martio's conjecture

We introduce a certain integrability condition for the reciprocal of the Jacobian determinant which guarantees the local homeomorphism property of quasiregular mappings with a small inner dilatation. This condition turns out to be sharp in the planar case. We also show that every branch point of a quasiregular mapping with a small inner dilatation is a Lebesgue point of the differential matrix of the mapping.

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