A sufficient condition for having big pieces of bilipschitz images of subsets of euclidean space in Heisenberg groups

Immo Hahlomaa

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arXiv · 1212.0687

A sufficient condition for having big pieces of bilipschitz images of subsets of euclidean space in Heisenberg groups

Immo Hahlomaa

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Abstract

In this article we extend a euclidean result of David and Semmes to the Heisenberg group by giving a sufficient condition for a $k$-Ahlfors-regular subset to have big pieces of bilipschitz images of subsets of $\R^k$. This Carleson type condition measures how well the set can be approximated by the Heisenberg $k$-planes at different scales and locations. The proof given here follow the paper of David and Semmes.

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Immo Hahlomaa. 2012-12-04. A sufficient condition for having big pieces of bilipschitz images of subsets of euclidean space in Heisenberg groups. https://arxiv.org/abs/1212.0687

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