Isoperimetric and concentration inequalities: Equivalence under curvature lower bound
Isoperimetric and concentration inequalities: Equivalence under curvature lower bound
It is well known that isoperimetric inequalities imply in a very general measure-metric-space setting appropriate concentration inequalities. The former bound the boundary measure of sets as a function of their measure, whereas the latter bound the measure of sets separated from sets having half the total measure, as a function …