The main aim of this book is to present recent developments of comparison geometry and
geometric analysis on Finsler manifolds in an accessible way to students and researchers …

For metric measure spaces satisfying the reduced curvature–dimension condition CD∗(K,
N) we prove a series of sharp functional inequalities under the additional “essentially …

In this paper we establish new stability properties for sequences of metric measure spaces
(X, di, mi) convergent in the measured Gromov-Hausdor sense (mGH for short). Even though …

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 …

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 …

On a Riemannian manifold, lower Ricci curvature bounds are known to be characterized by
geodesic convexity properties of various entropies with respect to the Kantorovich …

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 …

We study the qualitative stability of two classes of Sobolev inequalities on Riemannian
manifolds. In the case of positive Ricci curvature, we prove that an almost extremal function …

We prove that if M is a closed n-dimensional Riemannian manifold, n≥ 3, with Ric≥ n-1 and
for which the optimal constant in the critical Sobolev inequality equals the one of the n …

New lower bounds of the first nonzero eigenvalue of the weighted p-Laplacian are
established on compact smooth metric measure spaces with or without boundaries. Under …