Bounding the rank of Hermitian forms and rigidity for CR mappings of hyperquadrics

  title={Bounding the rank of Hermitian forms and rigidity for CR mappings of hyperquadrics},
  author={Dusty E. Grundmeier and Jiř{\'i} Lebl and Liz Raquel Vivas},
  journal={Mathematische Annalen},
Using Green’s hyperplane restriction theorem, we prove that the rank of a Hermitian form on the space of holomorphic polynomials is bounded by a constant depending only on the maximum rank of the form restricted to affine manifolds. As an application we prove a rigidity theorem for CR mappings between hyperquadrics in the spirit of the results of Baouendi–Huang and Baouendi–Ebenfelt–Huang. Given a real-analytic CR mapping of a hyperquadric (not equivalent to a sphere) to another hyperquadric… 
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