Key points are not available for this paper at this time.
We consider 3-manifolds given as Heegaard splittings M=H^-_ H^+ with the aim to describe the hyperbolic metric of M under topological conditions on the splitting guaranteeing that the manifold is hyperbolic. In particular, given a suitable "sufficiently incompressible" curve, we show (without appealing to Geometrization) that M is hyperbolic and we compute the length of in terms of the projection coefficients of the disk sets, up to a uniform multiplicative error.
Feller et al. (Tue,) studied this question.