Given any Γ= γ (S 1)⊂ R 2, image of a Lipschitz curve γ: S 1→ R 2, not necessarily injective,
we provide an explicit formula for computing the value of A (γ):= inf∫ B 1 (0)| det (∇ u)| dxu …

We establish the following uniformization result for metric spaces $ X $ of finite Hausdorff 2-
measure. If $ X $ is homeomorphic to a smooth 2-manifold $ M $ with non-empty boundary …

We compute an upper bound for the value of the $ L^ 1$-relaxed area of the graph of the
vortex map $ u: B_l (0)\subset\mathbb R^ 2\to\mathbb R^ 2$, $ u (x):= x/\vert x\vert $, $ x\neq …

Our main result gives an improved bound on the filling areas of curves in Banach spaces
which are not closed geodesics. As applications we show rigidity of Pu's classical systolic …

We introduce and study a notion of relative $1 $-homotopy type for Sobolev maps from a
surface to a metric space spanning a given collection of Jordan curves. We use this to …