In this paper we prove that in a metric measure space (X, d, 𝔪) verifying the measure
contraction property with parameters K∈ ℝ and 1< N<∞, any optimal transference plan …

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 …

In this paper, we give the characterization of metric measure spaces that satisfy synthetic
lower Riemannian Ricci curvature bounds (so called RCD*(K, N) spaces) with non-empty …

We give necessary and sufficient conditions that show that both the group of isometries and
the group of measure-preserving isometries are Lie groups for a large class of metric …

We extend the celebrated rigidity of the sharp first spectral gap under Ric≥ 0 to compact
infinitesimally Hilbertian spaces with non-negative (weak, also called synthetic) Ricci …

In this work, we generalize the results obtained in (J. Geom. Anal., 32 (6): Paper No. 173, 32,
2022), presenting some examples of $ CD (0, N) $ spaces having different dimensions in …

In this short note, we give a sufficient condition for almost smooth compact metric measure
spaces to satisfy the Bakry-Émery condition BE (K, N). The sufficient condition is satisfied for …

Abstract In Ketterer and Rajala (Potential Anal 42: 645–655, 2014) showed an example of
metric measure space, satisfying the measure contraction property MCP (0, 3), that has …

We introduce a more restrictive version of the strict CD (K, ∞) CD (K,∞)-condition, the so-
called very strict CD (K, ∞) CD (K,∞)-condition, and show the existence of optimal maps in …

We give an alternative proof for the fact that in n-dimensional Alexandrov spaces with
curvature bounded below there exists a unique optimal transport plan from any purely (n-1) …