Abstract
The main result implies that a proper convex subset of an irreducible higher rank symmetric space cannot have Zariski dense stabilizer.
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Kleiner, B., Leeb, B. Rigidity of invariant convex sets in symmetric spaces. Invent. math. 163, 657–676 (2006). https://doi.org/10.1007/s00222-005-0471-y
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DOI: https://doi.org/10.1007/s00222-005-0471-y