Mathematical Colloquium Minimal surfaces, isoperimetric inequalities and non-positive curvature

In this talk, I will begin with the classical isoperimetric inequality for closed curves in Euclidean space and its connection to the Plateau problem, as resolved by Douglas and Radó. The notion of non-positive curvature naturally enters the picture via the Gauss equation, which links the intrinsic and extrinsic geometry of surfaces. We then explore the relationship between the isoperimetric inequality and the intrinsic geometry of minimal discs. From there, the discussion extends beyond Euclidean ambient spaces to those of non-positive curvature, and from curves to higher-dimensional cycles.

This talk includes results from joint work with Cornelia Druţu, Urs Lang, Alexander Lytchak, Panos Papasoglu, and Stefan Wenger.