Isoperimetric inequalities on surfaces

Isoperimetric inequalities on surfaces

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Yannick Sire, ,John Hopkins University
Fine Hall 224

I will describe several recent results concerning extremal metrics and values of isoperimetric constants on different surfaces like the 2-sphere, the real projective plane or the Klein bottle. The idea is to find a metric realizing the supremum of a given eigenvalue over the whole set of Riemannian metrics on the surface. This problem (and its solutions) has a very strong link with the theory of harmonic maps.