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The FenchelNielsen Coordinates of Teichmüller Space
"... Abstract. We develop the FenchelNielsen coordinates for genus-g Teichmüller space. Specifically, we prove the existence and uniqueness of pairs of pants with all possible boundary components. We then examine the Bers pants-decomposition of a Riemann surface, and deduce that the genus-g FenchelNielse ..."
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Abstract. We develop the FenchelNielsen coordinates for genus-g Teichmüller space. Specifically, we prove the existence and uniqueness of pairs of pants with all possible boundary components. We then examine the Bers pants-decomposition of a Riemann surface, and deduce that the genus-g FenchelNielsen
Complex hyperbolic Fenchel-Nielsen coordinates
, 2005
"... Let Σ be a closed, orientable surface of genus g. It is known that the SU(2,1) representation variety of π1(Σ) has 2g − 3 components of (real) dimension 16g − 16 and two components of dimension 8g−6. Of special interest are the totally loxodromic, faithful (that is quasi-Fuchsian) representations. ..."
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. In this paper we give global real analytic coordinates on a subset of the representation variety that contains the quasi-Fuchsian representations. These coordinates are a natural generalisation of Fenchel-Nielsen coordinates on the Teichmüller space of Σ and complex Fenchel-Nielsen coordinates on the (classical
Computing Fenchel-Nielsen Coordinates in Teichmüller Shape Space
- COMMUNICATIONS IN INFORMATION AND SYSTEM
, 2009
"... Teichmüller shape space is a finite dimensional Riemannian manifold, where each point represents a class of surfaces, which are conformally equivalent, and a path represents a deformation process from one shape to the other. Two surfaces in the real world correspond to the same point in the Teichmül ..."
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Cited by 2 (1 self)
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in the Teichmüller space, only if they can be conformally mapped to each other. Teichmüller shape space can be used for surface classification purpose in shape modeling. This work focuses on the computation of the coordinates of high genus surfaces in the Teichmüller space. The coordinates are called as Fenchel-Nielsen
On Fenchel-Nielsen coordinates on Teichmüller spaces of surfaces of infinite type
, 2010
"... We introduce Fenchel-Nielsen coordinates on Teichmüller spaces of surfaces of infinite type. The definition is relative to a given pair of pants decomposition of the surface. We start by establishing conditions under which any pair of pants decomposition on a hyperbolic surface of infinite type ca ..."
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Cited by 11 (6 self)
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We introduce Fenchel-Nielsen coordinates on Teichmüller spaces of surfaces of infinite type. The definition is relative to a given pair of pants decomposition of the surface. We start by establishing conditions under which any pair of pants decomposition on a hyperbolic surface of infinite type
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"... Complex hyperbolic Fenchel-Nielsen coordinates. (English summary) ..."
Shearing coordinates and convexity of length functions on Teichmüller space
, 2009
"... We prove that there are Fenchel-Nielsen coordinates for the Teichmüller space of a finite area hyperbolic surface with respect to which the length functions are convex. ..."
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Cited by 6 (0 self)
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We prove that there are Fenchel-Nielsen coordinates for the Teichmüller space of a finite area hyperbolic surface with respect to which the length functions are convex.
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