For Riemannian manifolds with a measure (M, g, e− f dvolg) we prove mean curvature and
volume comparison results when the∞-Bakry-Emery Ricci tensor is bounded from below …

Let L= Δ−∇ ϕ⋅∇ be a symmetric diffusion operator with an invariant measure μ (dx)= e− ϕ
(x) dx on a complete non-compact Riemannian manifold M. We give the optimal conditions …

In this paper we take the perspective introduced by Case-Shu-Wei of studying warped
product Einstein metrics through the equation for the Ricci curvature of the base space. They …

We obtain new sharp isoperimetric inequalities on a Riemannian manifold equipped with a
probability measure, whose generalized Ricci curvature is bounded from below (possibly …

Following Bakry-Émery [1], see also [17, 3, 15, 12], given a Riemannian manifold (M, g) and
a C2-smooth function φ, M is said to have nonnegative∞-dimensional Bakry-Émery Ricci …

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

Dans cette Note, nous étendons la formule de Reilly au cas des opérateurs Laplaciens avec
dérive, et l'appliquons à l'étude d'estimées de valeurs propres pour de tels opérateurs sur …

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 …

In this paper, we study Perelman's\mathcal W-entropy formula for the heat equation
associated with the Witten Laplacian on complete Riemannian manifolds via the Bakry …

We develop the optimal transportation approach to modified log-Sobolev inequalities and to
isoperimetric inequalities. Various sufficient conditions for such inequalities are given. Some …