More than 30 years after the Harvey-Wells paper on complex approximation theory, we still do not know the answers to most of the relevant approximation-theoretic questions on, say, a smooth, compact 2-manifold (call it M) in C^2. Answering many of these questions boils down to examining the local polynomial convexity of M near those points where the (extrinsic) tangent space of M is a complex subspace of the ambient C^2. We shall quickly survey what is currently known, and then look at some recent progress based on examining the Maslov index.

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- Seminars for 2007

Last updated: 27 Feb 2024