Contact for zoom details: Christian Kaiser (kaiser@mpim-bonn.mpg.de)

Complete, simply connected Riemannian manifolds with non-positive sectional curvature are known as Cartan-Hadamard manifolds. These spaces are fundamental in global differential geometry and many of its interactions with analysis, topology and group theory. There is a long-standing conjeture that the isoperimetric inequality from Euclidean space, relating the volume of a bounded domain to the area of its perimeter, also holds in Cartan-Hadamard manifolds. The conjecture is currently open in all dimensions greater than four. We will prove that a closely related inequality, known as the Banchoff-Pohl inequality, holds in Cartan-Hadamard manifolds of all dimensions. We will also discuss the connections between this result and several other problems in geometry and analysis.

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