The question if a simply connected, complete manifold with non-positive sectional curvatures (a so-called Cartan-Hadamard manifold) satisfies the Euclidean isoperimetric inequality is widely open for dimensions greater or equal than five. We discuss the proofs in dimensions 2, 3 and 4 as well as a recent extension in the case of arbitrary codimension for 2-dimensional surfaces.
|Where?||PER 08 Phys 2.52
Chemin du Musée 3
|Contact||Department of Mathematics