On the nonexistence of bilipschitz parameterizations and geometric problems about $A_\infty$-weights

  title={On the nonexistence of bilipschitz parameterizations and geometric problems about \$A\_\infty\$-weights},
  author={S. Semmes},
  journal={Revista Matematica Iberoamericana},
  • S. Semmes
  • Published 31 August 1996
  • Mathematics
  • Revista Matematica Iberoamericana
How can one recognize when a metric space is bilipschitz equivalent to an Euclidean space? One should not take the abstraction of metric spaces too seriously here; subsets of Rn are already quite interesting. It is easy to generate geometric conditions which are necessary for bilipschitz equivalence, but it is not clear that such conditions should ever be sufficient. The main point of this paper is that the optimistic conjectures about the existence of bilipschitz parametrizations are wrong. In… 
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