Steve Buckley (NUI Maynooth)
Sphericalization and flattening
Abstract.
We discuss a certain family of conformal dilations that take unbounded
length spaces to bounded incomplete length spaces (sphericalization) and
vice versa (flattening). In particular, we study what happens to the
associated quasihyperbolic metric under sphericalization or flattening,
and give conditions under which sphericalization and flattening are
inverse processes. We also discuss the relationship between the boundary
at infinity under sphericalization and the ideal boundary. This talk is
based on work with Zoltan Balogh and with Simon Kokkendorff.
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