Research Interests:
Steve Buckley is interested in quasiconformal mappings, potential theory,
metric measure measures, Gromov hyperbolicity, geometric function theory,
and other fields in geometric and harmonic analysis. In particular, he is
interested in various types of Poincaré and Trudinger inequalities,
over Euclidean and non-Euclidean spaces, especially the connection between
such analytic inequalities and geometry.
He is also interested in metric spaces and metric measure spaces, where the
measure is often (but not always) doubling. Related to this, he is
attempting to achieve a better understanding of Gromov hyperbolicity for the
quasihyperbolic and related metrics.
Finally, he has also recently been looking at various spaces of analytic
functions. In particular, he has classified the nonlinear superposition
operators between various spaces of Besov and Dirichlet type. This involves
the use of both potential theory (non-standard Trudinger-type inequalities)
and geometric function theory (univalent Besov functions), and so links up
with his other interests.
