Local rigidity question for boundary actions of complex hyperbolic lattices

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Let a lattice in SU(1,n)SU(1,n) act on the boundary of complex hyperbolic space. Boundary-action rigidity question. Is the action of any lattice in SU(1,n)SU(1,n) on the boundary of complex hyperbolic space locally rigid? Work of Yue is cited as significant evidence, but the source leaves the question unresolved.

References

Primary source

David Fisher, “Local Rigidity of group actions: Past, Present, Future”, arXiv:math/0507455 (2007).

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