The Department of Mathematical Sciences presents
a colloquium by
Roger W. Barnard
Professor
of Mathematics and Statistics
Thursday, October 18, 2007
4 – 5 pm
Room 835
How far can you deform
a disk
under a convex map?
In this
talk, we will discuss how we apply variational
techniques
and special function
theory to verify some conjectures of
C. Pommerenke and
of D. Minda on the sharp upper bound for
the Schwarzian derivative of hyperbolically-convex maps. This
completes the
classification of the exteremal domains for the
Schwarzian
in all three classical geometries, hence,
answering
the question first posed in the ‘50s as to how
far
one can distort a disk under a convex map in
Euclidean,
spherical, and hyperbolic geometries.
Refreshments will be served at 3:30 pm
in the Faculty & Graduate Student
Lounge
Room 840 of the