Bi-Lipschitz Decomposition of Lipschitz functions into a Metric space

  title={Bi-Lipschitz Decomposition of Lipschitz functions into a Metric space},
  author={Raanan Schul},
  journal={Revista Matematica Iberoamericana},
  • R. Schul
  • Published 22 February 2007
  • Mathematics
  • Revista Matematica Iberoamericana
We prove a quantitative version of the following statement. Given a Lipschitz function f from the k-dimensional unit cube into a general metric space, one can decomposed f into a finite number of BiLipschitz functions f|_{F_i} so that the k-Hausdorff content of f([0,1]^k\setminus \cup F_i) is small. We thus generalize a theorem of P. Jones (1988) from the setting of R^d to the setting of a general metric space. This positively answers problem 11.13 in ``Fractured Fractals and Broken Dreams" by… 
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