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Random k-Surfaces

Francois Labourie
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Abstract

The main result is the construction of ergodic transversal measures of full support on the space of all k-surfaces of a compact hyperbolic 3-manifold. This space is a laminated space, each of its leaf being identified with a "complete" k-surface, i.e. a surface of constant (extrinsic) curvature k, where k belongs to ]0,1[. Elsewhere, this space has been shown to have chaotic properties mimicking those of the geodesic flow. This construction is achieved through a coding of the space.

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Francois Labourie. 2000-09-22. Random k-Surfaces. https://arxiv.org/abs/math/0009205

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