Mathematical Sciences: Research in Several Complex Variables and Application

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9622285 Lempert The proposed research lies in the area of several complex variables. The investigator wishes to study how the property of embeddability of Cauchy-Riemann manifolds behaves when the Cauchy-Riemann structure is perturbed. In addition, the investigator plans to study various properties of infinite dimensional complex manifolds: the inhomogeneous Cauchy-Riemann equations in Hilbert spaces, the extension of the Newlander-Nirenberg theorem and the Oka principle are among the topics pursued. Spaces based on complex numbers arise in many natural settings. For example, polynomial equations in general can not be solved unless one works in a (finite dimensional) complex space. The proposed research deals with abstract complex spaces and infinite dimensional complex spaces.