Speaker
Karl-Theodor Sturm
Description
We derive an explicit formula for the sectional curvature of the space M_0(X) of finite measures on a Riemannian manifold X. The space M_0(X) is equipped with the Hellinger-Kantorovich metric HK. Even in the case X = Rn, the curvature is comprised of two parts: the ‘lifted part’ is negative, and the ‘twisted part’ is positive. It will be analyzed in detail for the multidimensional torus.
Our general approach to sectional curvature in geodesic spaces also leads to new insights into the curvature of the space P_2(X) of probability measures on X equipped with the Kantorovich-Wasserstein metric W_2.