The maximum of the 1-measurement of a metric measure space

Isoperimetric rigidity and distributions of 1-Lipschitz functions

“…A more general and minute version of Theorem 1.9 for any mm-space is proved in §4 (see Theorem 4.1). A primitive version of Theorem 1.9 was obtain by the first named author [25].…”

Convergence of energy functionals and stability of lower bounds of Ricci curvature via metric measure foliation

“…Consider the sequence {S n ( √ n − 1)} n∈N , the map p n of (1.1), and the space X n in Section 1. X n pmG-converges to 1dimensional standard Gaussian space (R, | • |, γ) as n → ∞ (see [18,Lemma 3.9]), where γ is the 1-dimensional standard Gaussian measure (i.e. γ = γ 1 ).…”