31 citations · 145 across the 42 of their papers we have counts for
47 papers
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…
Semiclassical limit of Polyakov-Liouville measure and Q-Curvature Uniformization on even-dimensional manifolds
Maria Gordina, Eva Kopfer, Karl-Theodor Sturm
We study the semiclassical limit of the Polyakov-Liouville measure , which is a non-Gaussian measure on $H^{-\eps}(M)$ that has recently been extended from Riemann…
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…
Gradient and Transport Estimates for Heat Flow on Nonconvex Domains
Karl-Theodor Sturm
For the Neumann heat flow on nonconvex Riemannian domains , we provide sharp gradient estimates and transport estimates with a novel -dependence, for instance,…
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\…