Strongly Uniform Domains and Periodic Quasiconformal Maps

  title={Strongly Uniform Domains and Periodic Quasiconformal Maps},
  author={A. I. MathematicaVolumen and Shanshuang Yang},
An m-uniform domain in R n is, roughly, a domain such that any two maps from the i-sphere, 0 i m < n, into the domain can be homotoped to each other without going too far or too close to the boundary, when seen from the perspective of the images of the two maps. We establish several equivalent deenitions for m-uniform domains. We apply the theory by investigating the structure of the complementary domains of the xed point set of a quasiconformal reeection on the n-sphere S n. Moreover, we… CONTINUE READING