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 …

Abstract The Lp-Brunn–Minkowski theory for p≥ 1, proposed by Firey and developed by
Lutwak in the 90's, replaces the Minkowski addition of convex sets by its Lp counterpart, in …

We interpret the log-Brunn–Minkowski conjecture of Böröczky–Lutwak–Yang–Zhang as a
spectral problem in centro-affine differential geometry. In particular, we show that the Hilbert …

We study the quantitative stability of the quadratic optimal transport map between a fixed
probability density ρ and a probability measure μ on R d, which we denote T μ. Assuming …

We study the isoperimetric, functional and concentration properties of $ n $-dimensional
weighted Riemannian manifolds satisfying the Curvature-Dimension condition, when the …

Bakry–Émery Curvature Functions on Graphs Page 1 http://dx.doi.org/. /CJM--©Canadian
Mathematical Society Bakry–Émery Curvature Functions on Graphs David Cushing, Shiping …

We study several of the recent conjectures in regards to the role of symmetry in the
inequalities of Brunn–Minkowski type, such as the L_p L p-Brunn–Minkowski conjecture of …

We prove a new generalization of the Cheeger-Gromoll splitting theorem where we obtain a
warped product splitting under the existence of a line. The curvature condition in our splitting …

We study a Riemannian manifold equipped with a density which satisfies the Bakry-\'Emery
Curvature-Dimension condition (combining a lower bound on its generalized Ricci curvature …

Klartag recently gave a beautiful alternative proof of the isoperimetric inequalities of Lévy–
Gromov, Bakry–Ledoux, Bayle and Milman on weighted Riemannian manifolds. Klartag's …