The papers in this collection were presented at the First Ahlfors-Bers Colloquium--a conference held in the tradition of Lars Ahlfors and Lipman Bers. These conferences have been perpetuated to honor and carry on their work in the field of complex analysis, which so influenced their students, colleagues, and a new generation of mathematicians.

The papers cover complex analysis, Riemann surfaces, Teichmüller theory and hyperbolic manifolds: most of the works include original contributions to the field, and others survey various aspects of the field, including papers by Lennart Carleson, Clifford Earle, and Dennis Hejhal on the contributions of Lars Ahlfors.

Readership

Advanced graduate students and researchers working in the broad areas of Riemann surfaces, Teichmüller theory, hyperbolic geometry, and algebraic curves.

Table of Contents

• A. Basmajian -- Quasiconformal mappings and geodesics in the hyperbolic plane
• L. Carleson -- Lars Ahlfors and the Painlevé problem
• C. J. Earle -- The Ahlfors mollifiers
• C. J. Earle, F. P. Gardiner, and N. Lakic -- Asymptotic Teichmüller space, Part I: The complex structure
• C. J. Earle and S. Mitra -- Variation of moduli under holomorphic motions
• A. L. Epstein -- Effectiveness of Teichmüller modular groups
• H. M. Farkas and I. Kra -- Special sets of points on compact Riemann surfaces
• H. M. Farkas and I. Kra -- Three term theta identities
• D. M. Gallo -- Some remarks on the monodromy map
• F. P. Gardiner and L. Keen -- Coverings of Cantor sets
• F. P. Gardiner and N. Lakic -- Local boundary dilatation
• F. W. Gehring and K. Hag -- The Apollonian metric and quasiconformal mappings
• J. Gilman -- Complexity of a Turing machine discreteness algorithm
• D. A. Hejhal -- Kernel functions, Poincaré series, and LVA
• J. Huisman -- On components of spaces of \(\mathrm{PSL}_2{(\mathbb C)}\)-representations of extended quasifuchsian groups
• T. Jorgensen -- Composition and length of hyperbolic motions
• F. Luo -- Automorphisms of Thurston's space of measured laminations
• B. Maskit -- On spaces of classical Schottky groups
• H. A. Masur and Y. N. Minsky -- Unstable quasi-geodesics in Teichmüller space
• K. Matsuzaki -- Convergence of the Hausdorff dimension of the limit sets of Kleinian groups
• R. Riley -- Nielsen's algorithm to decide whether a group is Fuchsian
• H. Sato -- One-parameter families of extreme discrete groups for Jørgensen's inequality
• S. A. Wolpert -- Automorphic coefficient sums and the quantum ergodicity question