Jeremy Tyson (University of Illinois)
Branched quasiregular maps with optimal smoothness
Abstract.
Abstract: It is known that sufficiently smooth quasiregular maps are
unbranched. More precisely, every C^{n/(n-2)}-smooth quasiregular
map of R^n is locally invertible. By recent work of Bonk and
Heinonen, this exponent is sharp in dimension three. In this talk, I
will discuss the relation between smoothness and branching for
quasiregular maps in higher dimensions. For each positive $\epsilon$ we
construct a C^{2-\epsilon}-smooth quasiregular map of R^4 whose
branch set is a surface with a metric of snowflake type. This is joint
work with Robert Kaufman and Jang-Mei Wu.
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