31 citations · 145 across the 42 of their papers we have counts for
16 papers · 1 filter
Sectional Curvature for Kantorovich-Wasserstein and Hellinger-Kantorovich Geometries
Karl-Theodor Sturm
We derive an explicit formula for the sectional curvature of the space of finite measures on a Riemannian manifold M. The space is equipped with the Hel…
Gaussian Volume Functional, Integral Scalar Curvature, and Minimal Super-Ricci Flows
Marco Flaim, Erik Hupp, Karl-Theodor Sturm
We present a synthetic notion of scalar curvature (and its integral) for Riemannian manifolds and metric measure spaces, defined in terms of the initial slope of a Gaussian (double…
Synthetic approaches to Ricci flows
Matthias Erbar, Marco Flaim, Eric Hupp +3
We review different notions of synthetic Ricci flow that apply to time-dependent families of metric measure spaces and which are based on properties of the heat flow, ideas from op…
Bakry-Èmery, Hardy, and Spectral Gap Estimates on Manifolds with Conical Singularities
Karl-Theodor Sturm
We study spectral properties and geometric functional inequalities on Riemannian manifolds of dimension with (finite or countably many) conical singularities $\{z_i\}_{i\in\…
On gluing Alexandrov spaces with lower Ricci curvature bounds
Vitali Kapovitch, Christian Ketterer, Karl-Theodor Sturm
In this paper we prove that in the class of metric measure spaces with Alexandrov curvature bounded from below the Riemannian curvature-dimension condition with $K\in \m…
Rigidity of cones with bounded Ricci curvature
Matthias Erbar, Karl-Theodor Sturm
We show that the only metric measure space with the structure of an -cone and with two-sided synthetic Ricci bounds is the Euclidean space for integer. T…