Growth of horospheres in some Heintze spaces
Pablo Lessa (Universidad de la República de Uruguay)

In ongoing joint work with Gilles Courtois and Emiliano Sequeira we are exploring the volume growth of the horospheres of some homogeneous negatively curved spaces. The unit normal bundles of the horospheres are the strong stable manifolds of an Anosov flow (albeit on a non-compact space), so their volume growth is polynomial. We obtain an exact order of polynomial growth in some cases. Many interesting questions remain open.