Mathematical Sciences: Several Complex Variables

大卫巴雷特将工作的各种主题有关， 光滑有界的函数论和几何性质 域躺在n维复空间和更一般的 流形 几个研究课题涉及的问题， 在满足某些条件的域上， Levi形式的正性条件，但了解甚少 在更广泛的领域。关于近似的问题 标准函数空间理论，Bergman正则性 投影与双全纯映射和真映射的奇性 属于这一类。巴雷特还将调查问题 关于域和CR流形满足非常强 Levi形式的条件。这些问题包括全球 严格伪凸三维CR流形的嵌入 以及Levi-平坦超曲面的整体性质。

David Barrett will work on various topics relating to function theoretic and geometric properties of smooth bounded domains lying in n-dimensional complex space and in more general manifolds. Several of the research topics concern questions which are fairly well understood on domains which satisfy certain positivity conditions on the Levi form but are poorly understood on more general domains. The questions raised about approximation theory in standard function spaces, regularity of the Bergman projection, and singularities of biholomorphic and proper maps fall into this category. Barrett will also investigate problems relating to domains and CR manifolds satisfying very strong conditions on the Levi form. These include questions about global embedding of strictly pseudoconvex three dimensional CR manifolds and about global properties of Levi-flat hypersurfaces.