The goal of the paper is to give an optimal transport formulation of the full Einstein equations
of general relativity, linking the (Ricci) curvature of a space-time with the cosmological …

Let (M, g) be a smooth Riemannian manifold and G a compact Lie group acting on M
effectively and by isometries. It is well known that a lower bound of the sectional curvature of …

We characterize the null energy condition for an (n+ 1) (n+1)‐dimensional, time‐oriented
Lorentzian manifold in terms of convexity of the relative (n− 1) (n-1)‐Renyi entropy along …

We consider intermediate Ricci curvatures R ick on a closed Riemannian manifold M n.
These interpolate between the Ricci curvature when k= n-1 and the sectional curvature …

Some of the many good features of the Riemannian curvature-dimension condition is that it
corresponds, in the setting of smooth Riemannian manifolds, to a standard lower Ricci …

We prove a canonical variation-type result for submersion metrics with positive intermediate
Ricci curvatures. This can then be used in conjunction with surgery techniques to establish …

The goal of the present work is to study optimal transport on null hypersurfaces inside
Lorentzian manifolds. The challenge here is that optimal transport along a null hypersurface …

Abstract We prove Michael-Simon type Sobolev inequalities for n-dimensional submanifolds
in (n+ m)-dimensional Riemannian manifolds with nonnegative k th intermediate Ricci …

A new notion of displacement convexity on a matrix level is developed for density flows
arising from mean-field games, compressible Euler equations, entropic interpolation, and …

What is the optimal way to deform a projective hypersurface into another one? In this paper
we will answer this question adopting the point of view of measure theory, introducing the …