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Self-similar solutions to extension and approximation problems

By Robert Young

In 1979, Kaufman constructed a remarkable surjective Lipschitz map from a cube to a square whose derivative has rank 1 almost everywhere. In this talk, we will present some higher-dimensional generalizations of Kaufman's construction that lead to Lipschitz and Hölder maps with wild properties, including: topologically nontrivial maps from $S^m$ to $S^n$ with derivative of rank $n-1$, $\frac{2}{3}-\epsilon$--Hölder approximations of surfaces in the Heisenberg group, and Hölder maps from the disc to the disc that preserve signed area but approximate an arbitrary continuous map.

Information about the video

  • Date of recording 09/12/2022
  • Date of publication 30/12/2022
  • Institution IHES
  • Language English
  • Audience Researchers
  • Format MP4

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