V. Havin

Victor Havin : Approximation and uniqueness properties of harmonic differential forms


Lectures will be devoted to harmonic differential forms, a classical subject playing an important role in Analysis, Geometry and Mathematical Physics. Harmonic differential forms will be considered as multidimensional analogs of analytic functions of one complex variable. This point of view leads to interesting problems suggested by Complex Analysis and related to harmonic forms. Approximation properties of harmonic forms will be discussed (parallel to the theory of rational approximation in the complex plane). Another theme is uniqueness properties of harmonic forms. These themes are traditional and practically exhausted for harmonic forms of degree one in the plane (i.e. for complex analytic functions). But in higher dimensions (even in dimension three, i.e. for curl-free and divergence-free vector fields) they generate a lot of natural and hard questions (most of them open) and require new tools and ideas.


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