JournalsjemsVol. 13, No. 5pp. 1423–1475

A nonlinear Poisson transform for Einstein metrics on product spaces

  • Olivier Biquard

    Université Paris VI, France
  • Rafe Mazzeo

    Stanford University, USA
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Abstract

We consider the Einstein deformations of the reducible rank two symmetric spaces of noncompact type. If MM 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 MM.

Cite this article

Olivier Biquard, Rafe Mazzeo, A nonlinear Poisson transform for Einstein metrics on product spaces. J. Eur. Math. Soc. 13 (2011), no. 5, pp. 1423–1475

DOI 10.4171/JEMS/285