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The family hyperbolic metric for the plumbing variety $\{zw=t\}$ and the non holomorphic Eisenstein series $E(\zeta;2)$ are combined to provide an explicit expansion for the hyperbolic metrics for degenerating families of Riemann surfaces.
Some remarks on Teichmüller’s space of Riemann surfaces
Lars V. Ahlfors · 1961
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Partial differential equations
Lipman Bers, Fritz John, and Martin Schechter · 1964
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Spaces of degenerating Riemann surfaces
Lipman Bers · 1974
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Extension of the Weil-Petersson metric to the boundary of Teichmuller space
Howard Masur · 1976
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Fourier coefficients of the resolvent for a Fuchsian group
John D. Fay · 1977
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Complex manifolds and deformation of complex structures
Kunihiko Kodaira · 1986
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Projective structures with Fuchsian holonomy
William M. Goldman · 1987
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The complex analytic theory of Teichmüller spaces
Subhashis Nag · 1988
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The Selberg zeta function and a new Kähler metric on the moduli space of punctured Riemann surfaces
L. A. Takhtajan and P. G. Zograf · 1988
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Cut-and-paste deformations of Riemann surfaces
Scott A. Wolpert · 1988
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Spectral theory of automorphic functions and its applications
Alexei B. Venkov · 1990
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The hyperbolic metric and the geometry of the universal curve
Scott A. Wolpert · 1990
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A local index theorem for families of ∂ ¯ \overline{\partial} -operators on punctured Riemann surfaces and a new Kähler metric on their moduli spaces
L. A. Takhtajan and P. G. Zograf · 1991
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Infinite energy harmonic maps and degeneration of hyperbolic surfaces in moduli space
Michael Wolf · 1991
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Geometry and spectra of compact Riemann surfaces
Peter Buser · 1992
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An introduction to Teichmüller spaces
Y. Imayoshi and M. Taniguchi · 1992
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Spectral limits for hyperbolic surfaces. I, II
Scott A. Wolpert · 1992
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The curvature of the Petersson-Weil metric on the moduli space of Kähler-Einstein manifolds
Georg Schumacher · 1993
The asymptotic behavior of Eisenstein series and a comparison of the Weil-Petersson and the Zograf-Takhtajan metrics
Kunio Obitsu · 2001
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The Weil-Petersson isometry group
Howard Masur and Michael Wolf · 2002
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Classification of Weil-Petersson isometries
Georgios Daskalopoulos and Richard Wentworth · 2003
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Geometry of the Weil-Petersson completion of Teichmüller space
Scott A. Wolpert · 2003
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Canonical metrics on the moduli space of Riemann surfaces. I
Kefeng Liu, Xiaofeng Sun, and Shing-Tung Yau · 2004
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On the geometry of Weil-Petersson completion of Teichmüller spaces
Sumio Yamada · 2004
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Disappearance of cusp forms in special families
Scott A. Wolpert · 1994
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Automorphic forms on SL 2 ( 𝐑 ) {\rm SL}_{2}({\bf R})
Armand Borel · 1997
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Elliptic partial differential equations of second order
David Gilbarg and Neil S. Trudinger · 1998
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Metric spaces of non-positive curvature
Martin R. Bridson and André Haefliger · 1999
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Non-completeness of Zograf-Takhtajan’s Kähler metric for Teichmüller space of punctured Riemann surfaces
Kunio Obitsu · 1999
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On asymptotic Weil-Petersson geometry of Teichmüller Space of Riemann surfaces
Zheng Huang
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Canonical metrics on the moduli space of Riemann surfaces. II
Kefeng Liu, Xiaofeng Sun, and Shing-Tung Yau · 2005
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Weil-Petersson perspectives
Scott A. Wolpert · 2006
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Simple geodesics and Weil-Petersson volumes of moduli spaces of bordered Riemann surfaces
Maryam Mirzakhani · 2007
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Weil-Petersson volumes and intersection theory on the moduli space of curves
Maryam Mirzakhani · 2007
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Scott A. Wolpert · 2007
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