For a Lorentzian space measured by m in the sense of Kunzinger, Sämann, Cavalletti, and
Mondino, we introduce and study synthetic notions of timelike lower Ricci curvature bounds …

We establish topological regularity and stability of N–dimensional RCD (K, N) spaces (up to
a small singular set), also called noncollapsed RCD (K, N) in the literature. We also …

Metric measure spaces with synthetic Ricci bounds have attracted great interest in recent
years, accompanied by spectacular breakthroughs and deep new insights. In this survey, I …

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 …

We introduce the notions of 'super-Ricci flows' and 'Ricci flows' for time-dependent families
of metric measure spaces (X, dt, mt) t∈ I. The former property is proven to be stable under …

We develop the theory of tamed spaces which are Dirichlet spaces with distribution-valued
lower bounds on the Ricci curvature and investigate these from an Eulerian point of view. To …

In this paper we investigate Lott-Sturm-Villani's synthetic lower Ricci curvature bound on
Riemannian manifolds with boundary. We prove several measure rigidity results related to …

We study stability of the sharp spectral gap bounds for metric-measure spaces satisfying a
curvature bound. Our main result, new even in the smooth setting, is a sharp quantitative …

We will study metric measure spaces (X, d, m)(X, d, m) beyond the scope of spaces with
synthetic lower Ricci bounds. In particular, we introduce distribution-valued lower Ricci …

MONOTONICITY FORMULAS FOR PARABOLIC FREE BOUNDARY PROBLEMS ON
CONES∗ Page 1 Acta Mathematica Scientia, 2022, 42B(6): 2193–2203 https://doi.org/10.1007/s10473-022-0601-2 …