Mappings of finite distortion: Size of the branch set
Mappings of finite distortion: Size of the branch set
Abstract We study the branch set of a mapping between subsets of <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"><m:msup><m:mi>ℝ</m:mi><m:mi>n</m:mi></m:msup></m:math> {\mathbb{R}^{n}} , i.e., the set where a given mapping is not defining a local homeomorphism. We construct several sharp examples showing that the branch set or its image can have positive measure.