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

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

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