Filling minimality and Lipschitz-volume rigidity of convex bodies among integral current spaces

For zoom details contact: Stephen Stadler (stadler@mpim-bonn.mpg.de)

In this talk we consider metric fillings of boundaries of convex bodies. We show that convex bodies in Euclidean space are the unique minimal fillings of their boundary metrics among all integral current spaces. Prime examples of integral current spaces are compact oriented manifolds equipped with a metric that is bi-Lipschitz equivalent to a Riemannian (or Finsler) metric. We derive our filling result by using ideas of Burago--Ivanov and by proving that convex bodies enjoy the Lipschitz-volume rigidity property within the category of integral current spaces, which is well known in the smooth category. This is joint work with P. Creutz and E. Soultanis.