Strongly Uniform Domains and Periodic Quasiconformal Maps
نویسنده
چکیده
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 establish the (ordinary) uniformity of the complement of the xed point set of an arbitrary periodic quasiconformal homeomorphism of S n .
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