Mathematical Sciences: CR Geometry and Several Complex Variables

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Howard Jacobowitz will continue his work in Cauchy Riemann geometry and several complex variables. This an important area which involves both topological and analytic aspects of complex variable theory. Jacobowitz will bring geometric techniques to bear on the problems under investigation. A major theme throughout the research will be embedding problems for Cauchy Riemann structures. One aim of the research is to prove a more general boundary version of the Newlander-Nirenberg theorem and thereby obtain conditions for the local embeddability of more general CR structures. Another objective is to generalize an example of a locally but not globally embeddable CR structure. Jacobowitz will also continue his investigations of the prevalence of Fefferman spirals and their relations to points of zero Cartan curvature. A final topic is the study of the conformal class of certain singular two-dimensional metrics. Here he will associate with each metric a complex vector field and investigate the homogeneous solvability of the vector field.