Complex Manifolds and Hyperbolic Geometry.

Intro -- Contents -- Preface -- Self-maps of P2 with invariant elliptic curves -- Pants decompositions and the Weil-Petersson metric -- Dihedral groups acting on Jacobians -- Schwarz's lemma and Teichmüller contraction -- Barycentric extension and the Bers embedding for asymptotic Teichmüller space -- Symmetric rigidity for real polynomials with real critical points -- On theta constant identities and the evaluation of trigonometric sums -- On the genus of a random Riemann surface -- Earthquake curves -- Introduction -- 1. Homeomorphisms -- 1.1 Earthquakes on finite sets -- 1.2 Earthquakes on the circle -- 1.3 Construction of the measure -- 2. Earthquake Measures -- 2.1 Getting the earthquake from the measure -- 2.2 Recovering the measure -- 2.3 Recovering the homeomorphism -- 2.4 Measures that do not yield homeomorphisms -- 3. Quasisymmetric Homeomorphisms -- 3.1 Quasisymmetry implies Thurston bound -- 3.2 The finite ordinary differential equation -- 3.3 Thurston bound implies quasisymmetry -- 4. Ordinary Differential Equation -- 4.1 Differentiation of the curve -- 4.2 Uniqueness of solution -- 5. Smoothness Classes -- 5.1 Norms of tangent vectors -- 5.2 Scales of quadruples -- 5.3 Bounds on vanishing measures -- 5.4 Smooth homeomorphisms from vanishing measures -- 5.5 Vanishing measures from smooth homeomorphisms -- 5.6 Vanishing measures from vanishing initial vectors -- Efficient smooth quasiconformal mappings -- The Ehrenpreis conjecture and the moduli-rigidity gap -- Word sequences and intersection numbers -- A law of conservation of number for local Euler characteristics -- On families of algebraic curves with automorphisms -- Real surfaces, Riemann matrices and algebraic curves -- Approximation by meromorphic quadratic differentials -- On the topology of classical Schottky space -- Hyperbolic lego and algebraic curves in genus 2 and 3.

The Margulis region and continued fractions.

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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.