Abstract The Lott–Sturm–Villani Curvature-Dimension condition provides a synthetic notion
for a metric-measure space to have Ricci-curvature bounded from below and dimension …

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 …

This is a survey article on recent progress of comparison geometry and geometric analysis
on Finsler manifolds of weighted Ricci curvature bounded below. Our purpose is twofold …

By using optimal mass transport theory we prove a sharp isoperimetric inequality in CD (0,
N) metric measure spaces assuming an asymptotic volume growth at infinity. Our result …

The Lott-Sturm-Villani Curvature-Dimension condition provides a synthetic notion for a
metric-measure space to have Ricci-curvature bounded from below and dimension bounded …

We prove a sharp isoperimetric inequality for the class of metric measure spaces verifying
the synthetic Ricci curvature lower bounds Measure Contraction property ($\mathsf {MCP}(0 …

We consider a rigidity problem for the spectral gap of the Laplacian on an ${\rm
RCD}(K,\infty) $-space (a metric measure space satisfying the Riemannian curvature …

We prove that a Finsler spacetime endowed with a smooth reference measure whose
induced weighted Ricci curvature $\mathrm {Ric} _N $ is bounded from below by a real …

We investigate the rigidity problem for the logarithmic Sobolev inequality on weighted
Riemannian manifolds satisfying Ric _ ∞ ≥ K> 0 Ric∞≥ K> 0. Assuming that equality …

Abstract We establish the Bonnet–Myers theorem, Laplacian comparison theorem, and
Bishop–Gromov volume comparison theorem for weighted Finsler manifolds as well as …