Two-orbit manifolds with boundary
Résumé
Let $\rho_0$ be an action of a Lie group on a manifold with boundary that is transitive on the interior and on the boundary. We study the set of actions that are topologically conjugate to $\rho_0$, up to smooth or analytic change of coordinates. We show that in many cases, including the compactifications of negatively curved symmetric spaces, this set is infinite.
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