| Abstract: | Hörmander's L2 estimates on the ∂-equation on bounded pseudoconvex domains are a cornerstone of modern complex analysis. From the very beginning, attempts have been made (by Folland-Kohn, Shaw, Hörmander and others) to extend these L2 methods to appropriate classes of nonpseudoconvex domains. In this talk, we discuss an approach to the ∂-problem on an annulus between two weakly pseudoconvex domains which is inspired by Alexander-Pontrjagin duality in topology. This is ongoing joint work with Phil Harrington of Arkansas. |
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