| 研究実績の概要 |
I continued investigating the closed range property for the dbar operator on pseudoconvex,
unbounded domains in complex space. In particular, I have been working on the following questions on
such domains: (a) does the closed range property imply the vanishing of the L2 cohomology, and (b) after having given a sufficient condition of potential-theoretic type for dbar to have closed range, we are analyzing the property from a more geometric point of view. We know that if a domain in 1 dimension contains arbitrarily large disks then dbar can not have closed range. What the appropriate geometric condition is in higher dimensions is not clear yet at this point.
Both (a) and (b) are joint projects with J. Ruppenthal (University of Wuppertal, Germany).
I also started a project with T. Harz (University of Wuppertal, Germany) on the question whether a pseudoconvex domain in the two dimensional complex space of finite type 4 always admits a plurisubharmonic defining function. This is part of a long-term project of mine to understand convexity like conditions in the complex setting.
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