Geometry and Dynamics in Gromov Hyperbolic Metric Spaces

Tushar Das, University of Wisconsin, La Crosse, WI.David Simmons, University of York, United Kingdom.Mariusz Urbanski, University of North Texas, Denton, TX.

• Preliminaries: Algebraic hyperbolic spaces$\mathbb{R}$-trees, CAT(-1) spaces, and Gromov hyperbolic metric spacesMore about the geometry of hyperbolic metric spacesDiscretenessClassification of isometries and semigroupsLimit setsThe Bishop-Jones theorem: The modified Poincare exponentGeneralization of the Bishop-Jones theoremExamples: Schottky productsParabolic groupsGeometrically finite and convex-cobounded groupsCounterexamples$\mathbb{R}$-trees and their isometry groupsPatterson-Sullivan theory: Conformal and quasiconformal measuresPatterson-Sullivan theorem for groups of divergence typeQuasiconformal measures of geometrically finite groupsOpen problemsIndex of defined termsBibliography