Bers density conjecture for singly degenerate Kleinian groups

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Let SS be a closed surface, let AH(S)AH(S) denote the relevant space of Kleinian groups, and let BXB_X be the Bers slice with conformal boundary XX. For a Kleinian group Γ∈AH(S)\Gamma\in AH(S), write M=H3/ΓM=\mathbb{H}^3/\Gamma.

Bers density conjecture. If MM is singly degenerate, then Γ∈B‾X\Gamma\in\overline{B}_X, where XX is the conformal boundary of MM.

The conjecture concerns the density of geometrically finite structures in the boundary of a Bers slice. The source records proofs in several special cases, including geometrically finite groups, bounded geometry, and punctured-torus groups, and states that the paper handles unbounded geometry; its overall status is not specified in the supplied text.

References

Primary source

Kenneth Bromberg, “Projective structures with degenerate holonomy and the Bers density conjecture”, arXiv:math/0211402 (2002).

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