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1

Hyperbolic complex spaces. Berlin: Springer, 1998.

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2

Kobayashi, Shoshichi. Hyperbolic Complex Spaces. Berlin, Heidelberg: Springer Berlin Heidelberg, 1998. http://dx.doi.org/10.1007/978-3-662-03582-5.

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3

Kobayashi, Shoshichi. Hyperbolic complex spaces. Berlin: Springer, 1998.

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4

Lang, Serge. Introduction to complex hyperbolic spaces. New York: Springer-Verlag, 1987.

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5

Lang, Serge. Introduction to Complex Hyperbolic Spaces. New York, NY: Springer New York, 1987. http://dx.doi.org/10.1007/978-1-4757-1945-1.

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6

Mostly surfaces. Providence, R.I: American Mathematical Society, 2011.

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7

Ibragimov, Zair. Topics in several complex variables: First USA-Uzbekistan Conference on Analysis and Mathematical Physics, May 20-23, 2014, California State University, Fullerton, California. Providence, Rhode Island: American Mathematical Society, 2016.

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8

Aravinda, C. S. Geometry, groups and dynamics: ICTS program, groups, geometry and dynamics, December 3-16, 2012, CEMS, Kumaun University, Almora, India. Providence, Rhode Island: American Mathematical Society, 2015.

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9

Conformal dynamics and hyperbolic geometry: A conferece in honor of Linda Keen's 70th birthday, October 22-24, 2010, Graduate School and University Center of CUNY, New York, New York. Providence, R.I: American Mathematical Society, 2010.

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10

Bergeron, Nicolas. Spectre automorphe des variétés hyperboliques et applications topologiques. Paris: Société mathématique de France, 2005.

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11

Riemann surfaces by way of complex analytic geometry. Providence, R.I: American Mathematical Society, 2011.

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12

1975-, Champanerkar Abhijit, ed. Interactions between hyperbolic geometry, quantum topology, and number theory: Workshop, June 3-13, 2009, conference, June 15-19, 2009, Columbia University, New ork, NY. Providence, R.I: American Mathematical Society, 2011.

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13

Farb, Benson, and Dan Margalit. Moduli Space. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691147949.003.0013.

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This chapter focuses on the moduli space of Riemann surfaces. The moduli space parameterizes many different kinds of structures on Sɡ, such as isometry classes of hyperbolic structures on S, conformal classes of Riemannian metrics on S, biholomorphism classes of complex structures on S, and isomorphism classes of smooth algebraic curves homeomorphic to S. The chapter first considers the moduli space as the quotient of Teichmüller space before discussing the moduli space of the torus. It then examines the theorem (due to Fricke) that Mod(S) acts properly discontinuously on Teich(S), with a finite-index subgroup of Mod(S) acting freely such that M(S) is finitely covered by a smooth aspherical manifold. The chapter also looks at Mumford's compactness criterion, which describes what it means to go to infinity in M(S), and concludes by showing that M(Sɡ) is very close to being a classifying space for Sɡ-bundles.
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14

Kobayashi, Shoshichi. Hyperbolic Complex Spaces. Springer Berlin / Heidelberg, 2010.

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15

Kobayashi, Shoshichi. Hyperbolic Complex Spaces. Springer London, Limited, 2013.

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16

Lang, Serge. Introduction to Complex Hyperbolic Spaces. Springer, 2010.

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17

Lang, Serge. Introduction to Complex Hyperbolic Spaces. Springer London, Limited, 2013.

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18

Michihiko, Fujii, ed. Complex analysis and geometry of hyperbolic spaces. [Kyoto]: Kyōto Daigaku Sūri Kaiseki Kenkyūjo, 2006.

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19

Farb, Benson, and Dan Margalit. Teichmuller Geometry. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691147949.003.0012.

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This chapter focuses on the metric geometry of Teichmüller space. It first explains how one can think of Teich(Sɡ) as the space of complex structures on Sɡ. To this end, the chapter defines quasiconformal maps between surfaces and presents a solution to the resulting Teichmüller's extremal problem. It also considers the correspondence between complex structures and hyperbolic structures, along with the Teichmüller mapping, Teichmüller metric, and the proof of Teichmüller's uniqueness and existence theorems. The fundamental connection between Teichmüller's theorems, holomorphic quadratic differentials, and measured foliations is discussed as well. Finally, the chapter describes the Grötzsch's problem, whose solution is tied to the proof of Teichmüller's uniqueness theorem.
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20

Topology, complex analysis and arithmetic of hyperbolic spaces. [Kyoto]: Kyōto Daigaku Sūri Kaiseki Kenkyūjo, 2007.

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21

Marden, Albert. Hyperbolic Manifolds: An Introduction in 2 and 3 Dimensions. Cambridge University Press, 2016.

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22

Marden, Albert. Hyperbolic Manifolds: An Introduction in 2 and 3 Dimensions. Cambridge University Press, 2016.

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23

Marden, Albert. Hyperbolic Manifolds: An Introduction in 2 and 3 Dimensions. Cambridge University Press, 2015.

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24

Conformal and Harmonic Measures on Laminations Associated with Rational Maps (Memoirs of the American Mathematical Society). American Mathematical Society, 2005.

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25

Spectre Automorphe Des Varietes Hyperboliques Et Applications Topologiques. Amer Mathematical Society, 2006.

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