Rigidity of locally Hermitian symmetric rank one manifolds of infinite volume

  • Boris Apanasov (University of Oklahoma)
E2 10 (Leon-Lichtenstein)


We address G.D.Mostow, L.Bers and S.L.Krushkal questions on uniqueness of conformal/spherical CR structures on the sphere at infinity of non-compact (Hermitian) symmetric rank one spaces compatible with the action of a discrete isometry group. We construct such non-rigid discrete isometry groups whose quotients have infinite volumes and whose non-trivial deformations are induced by equivariant homeomorphisms of the (Hermitian) symmetric space with bounded horizontal distortion. This non-rigidity is related to non-ergodic dynamics of our discrete isometry group actions on the limit set which could be the whole sphere at infinity.

Katharina Matschke

MPI for Mathematics in the Sciences Contact via Mail

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