Dynamics on the unit disk: Short geodesics and simple cycles

Dynamics on the unit disk: Short geodesics and simple cycles

Ribbon R-trees and holomorphic dynamics on the unit disk

Simple heuristics for unit disk graphs

Unit disk graphs are intersection graphs of circles of unit radius in the plane. We present simple and provably good heuristics for a number of classical NP-hard optimization problems on unit disk graphs. The problems considered include maximum independent set, minimum vertex cover, minimum coloring and minimum dominating set. We also present an on-line coloring heuristic which achieves a compe...

New results on p-Carleson measures and some related measures in the unit disk

We provide some new sharp embeddings for p-Carleson measures and some related measures in the unit disk of the complex plane.

Weierstrass Points and Simple Geodesics

We investigate the set of tangent vectors at a Weierstrass point tangent to complete simple geodesics, which we think of as an innnitesimal version of the Birman Series set, showing that they are a Cantor set of Haus-dorr dimension 1. The gaps in the Cantor set are classiied in terms of the topological behavior of those geodesics tangent to the vector bounding them and deduce 3 new identities f...