1)Quasiminimal sets for Hausdorff measure 2)Analytic capacity, Menger curvature, and rectifiability

speaker: Guy David (Université de Paris-Sud)

abstract: Quasiminimal sets for Hausdorff measure

I will try to explain with two simple examples why the notion of quasiminimal sets introduced by Almgren can be useful when one tries to minimize a functional with a surface term, under a topological constraint.

Analytic capacity, Menger curvature, and rectifiability

In the first lecture I will try to describe the connections between analytic capacity, singular integral operators, and (a little) Menger curvature. Recall that X. Tolsa recently characterized vanishing analytic capacity in geometrical terms.

In the second lecture I should insist more on relations between Menger curvature, the Cauchy kernel, and rectifiability.

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