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A nonlinear Poisson transform for Einstein metrics on product spaces

Olivier Biquard, Rafe Mazzeo (2011)

Journal of the European Mathematical Society

We consider the Einstein deformations of the reducible rank two symmetric spaces of noncompact type. If M is the product of any two real, complex, quaternionic or octonionic hyperbolic spaces, we prove that the family of nearby Einstein metrics is parametrized by certain new geometric structures on the Furstenberg boundary of M .

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