Concentration and isoperimetry are equivalent assuming curvature lower bound

Emanuel Milman

Comptes Rendus. Mathématique, Volume 347 (2009) no. 1 p. 73-76

Uniform tail-decay of Lipschitz functions implies Cheeger's isoperimetric inequality under convexity assumptions

Emanuel Milman

Comptes Rendus. Mathématique, Volume 346 (2008) no. 17 p. 989-994