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2008 Quakebend deformations in complex hyperbolic quasi-Fuchsian space
Ioannis D Platis
Geom. Topol. 12(1): 431-459 (2008). DOI: 10.2140/gt.2008.12.431

Abstract

We study quakebend deformations in complex hyperbolic quasi-Fuchsian space Q(Σ) of a closed surface Σ of genus g>1, that is the space of discrete, faithful, totally loxodromic and geometrically finite representations of the fundamental group of Σ into the group of isometries of complex hyperbolic space. Emanating from an –Fuchsian point ρQ(Σ), we construct curves associated to complex hyperbolic quakebending of ρ and we prove that we may always find an open neighborhood U(ρ) of ρ in Q(Σ) containing pieces of such curves. Moreover, we present generalisations of the well known Wolpert–Kerckhoff formulae for the derivatives of geodesic length function in Teichmüller space.

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Ioannis D Platis. "Quakebend deformations in complex hyperbolic quasi-Fuchsian space." Geom. Topol. 12 (1) 431 - 459, 2008. https://doi.org/10.2140/gt.2008.12.431

Information

Received: 23 February 2007; Accepted: 6 December 2007; Published: 2008
First available in Project Euclid: 20 December 2017

zbMATH: 1153.30038
MathSciNet: MR2390350
Digital Object Identifier: 10.2140/gt.2008.12.431

Subjects:
Primary: 32G05
Secondary: 32M05

Rights: Copyright © 2008 Mathematical Sciences Publishers

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