Quasiconformal maps in metric spaces with controlled geometry

  title={Quasiconformal maps in metric spaces with controlled geometry},
  author={Juha M. Heinonen and Pekka Koskela},
  journal={Acta Mathematica},
This paper develops the foundations of the theory of quasiconformal maps in metric spaces that satisfy certain bounds on their mass and geometry. The principal message is that such a theory is both relevant and viable. The first main issue is the problem of definition, which we next describe. Quasiconformal maps are commonly understood as homeomorphisms that distort the shape of infinitesimal balls by a uniformly bounded amount. This requirement makes sense in every metric space. Given a… 

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From local to global in quasiconformal structures.

  • J. HeinonenP. Koskela
  • Mathematics
    Proceedings of the National Academy of Sciences of the United States of America
  • 1996
We exhibit a large class of metric spaces whose infinitesimal quasiconformal structure is strong enough to capture the global quasiconformal structure. A sufficient condition for this to happen is