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In this talk, I shall explain the existence, in non-positively curved spaces, of a 2-dimensional isoperimetric gap, similar to the one in dimension 1, i.e. for the filling of loops by discs. The argument is based on the thinness of a particular type of tetrahedra, the minimal tetrahedra. This is joint work with Urs Lang, Panos Papasoglu and Stephan Stadler.
Sam Hughes