Niagara Falls, 2 - 5 décembre 2016
In this talk, we address an analogous problem with the data consisting of areas of minimal surfaces rather than of lengths of geodesics. More precisely, for any simple closed curve on the boundary, we are given the area of the area-minimizing surface(s) bounded by the curve. We show that for certain compact, connected Riemannian 3-manifolds with boundary this information uniquely determined the metric in the interior up to diffeomorphisms that fix the boundary.
(joint work with S. Alexakis and A. Nachman.)