The Dimension Conjecture for 2-Nondegenerate Hypersurfaces

Abstract

The dimension conjecture in CR geometry is proved for 2-nondegenerate real-analytic hypersurfaces with sign-definite Levi form. Namely, it is proved that, in the indicated class of hypersurfaces in ${\mathbb{C}}^N$, the maximum dimension of finite-dimensional Lie algebras of infinitesimal holomorphic automorphisms is strictly smaller than the corresponding dimension for nondegenerate hyperquadrics in ${\mathbb{C}}^N$.