In the Tradition of Ahlfors–Bers, VII.

Cover -- Title page -- Contents -- Preface -- List of Plenary Lectures -- The complex geometry of Teichmüller spaces and bounded symmetric domains -- 1. Introduction -- 2. The setting -- 3. The Kobayashi metric -- 4. Main results -- 5. Preliminaries in Teichmüller theory -- 6. Holomorphic rigidity -- 7. Extremal length geometry -- 8. Final remarks -- References -- Pseudo-Anosovs optimizing the ratio of Teichmüller to curve graph translation length -- 1. Introduction -- 2. Background -- 3. Ratio optimizers via QI trees -- 4. Counting ratio optimizers in a Teichmüller Disk -- 5. Ratio optimizers in the Johnson filtration and point pushing subgroups -- References -- Handlebody subgroups in a mapping class group -- 1. Introduction -- 2. Preliminaries -- 3. Coarse fixed sets and free products -- 4. Example on a tree -- 5. Example on \C( ) and proof of theorem -- 6. Prime pseudo-Anosov elements -- 7. Invariable generation -- References -- The convex real projective orbifolds with radial or totally geodesic ends: A survey of some partial results -- 1. Introduction -- 1.1. Preliminary -- 1.2. Main results -- 1.3. Remarks -- 1.4. Outline -- 1.5. Acknowledgement -- 2. Preliminary -- 2.1. Basic definitions -- 2.1.1. Topological notation -- 2.1.2. The Hausdorff metric -- 2.1.3. Real projective structures -- 2.1.4. End structures -- 2.1.5. Horospherical ends -- 2.1.6. Deformation spaces and the space of holonomy homomorphisms -- 2.1.7. The end restrictions -- 2.1.8. Character spaces of relevance -- 2.2. Oriented real projective structures -- 2.3. The local homeomorphism theorems -- 3. Convex real projective structures -- 3.1. Metrics -- 3.2. Convexity and convex domains -- 3.3. The duality -- 4. The end theory -- 4.1. p-ends, p-end neighborhoods, and p-end fundamental groups -- 4.2. The admissible groups -- 4.3. The admissible ends.

5. The relative hyperbolicity of ₁(\orb) and the strict convexity -- 5.1. SPC-structures and its properties -- 5.2. Bowditch's method -- 5.3. Converse -- 5.4. Strict SPC-structures deform to strict SPC-structures. -- 6. The openness and closedness in character varieties -- 6.1. The semi-algebraic properties of \rep^{ }( ₁( ),\PGL( +1,\bR)) and related spaces -- 6.1.1. Main theorems -- 6.2. Openness -- 6.3. The closedness of convex real projective structures -- 6.4. Nicest cases -- References -- A gluing theorem and applications in subspaces of the universal Teichmüller space -- 1. Introduction -- 2. Proof of the gluing theorem -- 3. Proofs of Theorems 2 and 3 -- References -- Extremal length and uniformization -- Introduction -- 1. Riemann surfaces, weak measured foliations and the Dirichlet integral -- 2. Conformal metrics and conjugate differentials -- 3. Pulling back a weak measured foliaton -- 4. Intersection number and the Cauchy-Schwarz inequality -- 5. Extremal length of annuli -- 6. Moduli of curve families on a Riemann surface -- 7. Strebel's variational technique -- 8. Uniformization -- 9. Weyl's lemma -- 10. The long ray, the long line and the long cylinder -- References -- Winding and unwinding and essential intersections in ℍ³ -- 1. Introduction -- 2. Background and Terminology -- 3. \HH²: The Model Group -- 4. \HH³: Generalized ESI's -- 5. Winding Groups -- References -- The 1-2 model -- 1. Origin of the \ot model -- 2. Definition of the \ot model -- 3. The dimer, Ising, and polygon models -- 4. Phase transition -- Acknowledgements -- References -- Meromorphic quadratic differentials with complex residues and spiralling foliations -- 1. Introduction -- 2. Preliminaries -- 3. Measured foliations with centers -- 4. Model maps and cylinder ends -- 5. Proof of Theorem 1.2 -- References.

Quasi-isometric rigidity of the class of convex-cocompact Kleinian groups -- 1. Introduction -- 2. Hyperbolizable 3-manifolds -- 3. Hyperbolicity -- 4. Canonical splittings -- 5. Strong accessibility -- 6. Quasi-isometric rigidity -- 7. Examples -- References -- Variation of moduli under continuous motions -- 1. Statements of the results -- 2. Background material -- 3. The proofs -- References -- Systolic surfaces of arithmetic hyperbolic 3-manifolds -- 1. Introduction -- 2. Notation -- 3. Arithmetic Fuchsian and Kleinian groups and their covolumes -- 4. Proof of Theorem A -- 5. Proof of Theorem B -- 6. Proof of Theorem C -- References -- Extremal length functions are log-plurisubharmonic -- 1. Introduction -- 2. Notation -- 3. Coordinates via representations of the odd cohomology -- 4. Families of quadratic differentials with prescribed vertical foliation -- 5. Levi forms and Plurisubharmonicity of Extremal length functions -- 6. Geometric interpretation of realizations of tangent vectors -- 7. Appendix -- References -- Back Cover.

The Ahlfors-Bers Colloquia commemorate the mathematical legacy of Lars Ahlfors and Lipman Bers. The core of this legacy lies in the fields of geometric function theory, Teichmüller theory, hyperbolic geometry, and partial differential equations. Today we see the influence of Ahlfors and Bers on algebraic geometry, mathematical physics, dynamics, probability, geometric group theory, number theory and topology. Recent years have seen a flowering of this legacy with an increased interest in their work. This current volume contains articles on a wide variety of subjects that are central to this legacy. These include papers in Kleinian groups, classical Riemann surface theory, Teichmüller theory, mapping class groups, geometric group theory, and statistical mechanics.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.