On estimates for the tangential Cauchy-Riemann operator on weakly pseudoconvex CR manifolds

Mikeung Park, Purdue University

Abstract

A smooth real manifold M is called a CR manifold if there exists an integrable subbundle of the complexified tangent bundle $\doubc T(M)$ with almost complex structure. Kohn has a result on a local estimate for the tangential Cauchy-Riemann operator $\overline{\partial}\sb{b}$ on 3-dimensional strongly pseudoconvex CR manifold. In this thesis, we obtain a global estimate for the tangential Cauchy-Riemann operator $\overline{\partial}\sb{b}$ on 3-dimensional weakly pseudoconvex CR manifold M via microlocal analysis on vector bundles of M utilizing pseudodifferential operators.

Degree

Ph.D.

Advisors

Catlin, Purdue University.

Subject Area

Mathematics

COinS