Department of Mathematics

Analysis and PDE

  •  Stretching and Rotation Sets of Quasiconformal Maps
  •  10/11/2017
  •  4:10 PM - 5:00 PM
  •  C517 Wells Hall
  •  Tyler Bongers, MSU

Quasiconformal maps in the plane are orientation preserving homeomorphisms that satisfy certain distortion inequalities; infinitesimally, they map circles to ellipses of bounded eccentricity. Such maps have many useful geometric distortion properties, and yield a flexible and powerful generalization of conformal mappings. In this work, we study the singularities of these maps, in particular the sizes of the sets where a quasiconformal map can exhibit given stretching and rotation behavior. We improve results by Astala-Iwaniec-Prause-Saksman and Hitruhin to give examples of stretching and rotation sets with non-sigma-finite measure at the appropriate Hausdorff dimension.

 

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Michigan State University
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