Length of ray-images under conformal maps

Images of eigenvalue distributions under power maps

In [6], it was shown that if U is a random n×n unitary matrix, then for any p ≥ n, the eigenvalues of Up are i.i.d. uniform; similar results were also shown for general compact Lie groups. We study what happens when p < n instead. For the classical groups, we find that we can describe the eigenvalue distribution of Up in terms of the eigenvalue distributions of smaller classical groups; the ear...

Invariants of objects and their images under surjective maps

We examine the relationships between the differential invariants of objects and of their images under a surjective map. We analyze both the case when the underlying transformation group is projectable and hence induces an action on the image, and the case when only a proper subgroup of the entire group acts projectably. In the former case, we establish a constructible isomorphism between the al...

Conformal Maps and Minimal Surfaces

Conformal Images of Carleson Curves

We show that if γ is a curve in the unit disk, then arclength on γ is a Carleson measure iff the image of γ has finite length under every conformal map onto a domain with rectifiable boundary. Date: July 27, 2012. 1991 Mathematics Subject Classification. Primary: 30C62 Secondary:

Extremal Length and Conformal Capacityo