Bending formulae for convex hull boundaries
The action of a Kleinian group \(G\) on \(\widehat C\) decomposes into a regular set \(\Omega(G)\) on which the action of properly discontinuous, and a limit set \(\Lambda(G)\) on which the action is minimal. The boundary \(\partial C(G)\) of the hyperbolic convex hull of \(\Lambda\) in the hyperbolic space \(H^3\) is a pleated surface: a union of pieces of flat planes which meets along a geodesic bending line. The paper under review, as the title says, gives some bending formulae. It deals with the special case when some boundary component of \(\partial C/G\) is either a punctured torus or a four times punctured sphere, pleated along a simple closed curve \(\gamma\). The authors obtain an exact formula for the bending and shearing along \(\gamma\). Then they study three exmaples: the Maskit embedding of the punctured torus, the Riley slice for the four punctured sphere and quasi-Fuchsian punctured tori.
scientific article; zbMATH DE number 871560
scientific article