Deformation of CR structures and Spectral Stability of the Kohn Laplacian (Siqi Fu - IHES et Rutgers University-Camden)

Deformation of complex structures has been studied extensively since the classical work of
Kodaira and Spencer in the 1950s. In this talk, we study the interplay between stability of embeddings
of pseudoconvex CR manifolds and spectral stability of the Kohn Laplacian. We establish an equivalence
between stability of embeddings of pseudoconvex CR manifolds and a uniform spectral gap property for
the Kohn Laplacian and apply it to study stability of embeddings of 3-dimensional compact pseudoconvex
CR manfolds of finite type into complex Euclidean space of dimension 2. This talk is based on a joint
work with H. Jacobowitz and W. Zhu.