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Let $\mathcal{P}_2(M)$ be the 2-Wasserstein space over some Riemannian manifold $(M,g)$ (connected, complete, and without boundary). Let $\mathcal{FP}_2(M,n)$ be the subspace of probability measures ...

Let $A \subset \mathbb{R}^n$ be a region having the same volume as an $n$ dimensional ball $B^n_R$ with radius $R$ centring at the origin. Isoperimetric inequality says: $ Vol_{n-1} \partial A \geq ...