Institute for Mathematical Sciences
Preface to "On Actions of Epimorphic Subgroups on Homogeneous Spaces" and "Unique Ergodicity on Compact Homogeneous Spaces"
Abstract: This short note serves as a joint introduction to the papers ``On Actions of Epimorphic Subgroups on Homogeneous Spaces"
by Nimesh Shah and Barak Weiss (Stony Brook IMS preprint 1999/7b)
and ``Unique Ergodicity on Compact Homogeneous Spaces" by Barak
Weiss. For the benefit of the readers who are not experts in
the theory of subgroup actions on homogeneous spaces I have
prefaced the papers with some general remarks explaining and
motivating our results, and the connection between them.
The remarks are organized as a comparison between facts which had
been previously known about the action of the geodesic and
horocycle flow on finite-volume Riemann surfaces -- the
simplest nontrivial example that falls into our framework --
and our results on subgroup actions on homogeneous spaces.
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