On the shape of bers-maskit slices

Yohei Komori, Jouni Parkkonen

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

We consider complex one-dimensional Bers-Maskit slices through the deformation space of quasifuchsian groups which uniformize a pair of punctured tori. In these slices, the pleating locus on one of the components of the convex hull boundary of the quotient three-manifold has constant rational pleating and constant hyperbolic length. We show that the boundary of such a slice is a Jordan curve which is cusped at a countable dense set of points. We will also show that the slices are not vertically convex, proving the phenomenon observed numerically by Epstein, Marden and Markovic.

Original languageEnglish
Pages (from-to)179-198
Number of pages20
JournalAnnales Academiae Scientiarum Fennicae Mathematica
Volume32
Issue number1
Publication statusPublished - 2007
Externally publishedYes

Fingerprint

Slice
Three-manifolds
Jordan Curve
Convex Hull
Set of points
Locus
Countable
Torus
Quotient

Keywords

  • End invariants
  • Kleinian groups
  • Pleating coordinates
  • Punctured torus groups
  • Teichmüller space

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

On the shape of bers-maskit slices. / Komori, Yohei; Parkkonen, Jouni.

In: Annales Academiae Scientiarum Fennicae Mathematica, Vol. 32, No. 1, 2007, p. 179-198.

Research output: Contribution to journalArticle

Komori, Yohei ; Parkkonen, Jouni. / On the shape of bers-maskit slices. In: Annales Academiae Scientiarum Fennicae Mathematica. 2007 ; Vol. 32, No. 1. pp. 179-198.
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