Based on that observation, he generalizes the localization technique from convex geometry to the setting of Riemannian manifolds with Ricci curvature that is

bounded from below.

Among the topics are calculus and heat flow in metric measure spaces and spaces with Riemannian curvature

bounded from below, Ma-Trudinger-Wang curvature and regularity of optimal transport maps, and a proof of Bobkov's spectral bound for convex domains via Gaussian fitting and free energy estimation.

n] be an n-dimensional complete Riemannian manifold whose Ricci curvature is

bounded from below and u : [[SIGMA].

n]) is descending and

bounded from below in F(X) (by (c02)); hence, a Cauchy one.

The size-Ramsey number of H can be

bounded from below in terms of [Tau](H) and the maximum degree [Delta] (H) of a graph H.

Furthermore, if utility is bounded from below, then (7) can be used to show that

is increasing for utility functions which are bounded from below.