Geometry & Topology Seminar

Andrew Nicas, McMaster University

"Metric transforms yielding Gromov hyperbolic spaces"

A real valued function f of one variable is called a metric transform if for every metric space (X, d) the composition d' = f d is also a metric on X.  We show "metric transform rigidity" for roughly geodesic Gromov hyperbolic spaces, that is, if (X, d) is any metric space containing a rough geodesic ray and f is an approximately nondecreasing, unbounded metric transform such that the transformed space (X, d') is Gromov hyperbolic and roughly geodesic then f must be an approximate dilation and the original space (X, d) is Gromov hyperbolic and roughly geodesic.  Our techniques are elementary and the basic concepts involved will be explained. This is joint work with George Dragomir.

MC 5403