34 videos

34 videos

4 videos

4 videos

2022 - Francophone Computer Algebra Days - Journées nationales de calcul formel

00:00:00 / 00:00:00

Self-similar solutions to extension and approximation problems

Appears in collection : Not Only Scalar Curvature Seminar

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.

• Date of recording 12/9/22
• Date of publication 12/30/22
• Institution IHES
• Language English
• Audience Researchers
• Format MP4

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