The stability of embeddings of Cauchy-Riemann manifolds

Hua-Lun Li, Purdue University

Abstract

The Cauchy-Riemann (CR for short) manifolds are geometric models of rather general first order linear systems of partial differential equations. It is one of the main objects studied in several complex variables. Specially three dimensional CR manifolds; it has been known for about thirty years that (among the so called hypersurface type CR manifolds) these are the hardest to understand. A CR manifold is called embeddable if it can be realized in some Euclidean complex space. In the past five years much effort has been spent on describing the moduli space of embeddable CR manifolds. Several phenomena indicate the stability problem we considered here is crucial in this regard. The main object in this thesis is to formulate a stability theorem for strictly pseudoconvex manifolds with certain conditions. Then by using this theorem we are able to give affirmative answer for three dimensional strictly pseudoconvex CR manifolds in positive line bundles over Riemann sphere. We hope our approach will lead to more general situations. Other things studied in this thesis are a weaker stability theorem for three dimensional strictly pseudoconvex CR manifolds in positive line bundles over tori and a theorem about lower dimensional CR embeddings.

Degree

Ph.D.

Advisors

Lempert, Purdue University.

Subject Area

Mathematics

COinS