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questions
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The composition of optimal transport maps is no longer an optimal transport map
Let $X,Y,Z$ be metric spaces. Let $\mu,\nu,\omega$ be the probability measures on $X,Y,Z$, respectively. Moreover, assume all three measures vanish on small sets. Assume $T:X\to Y$ is the optimal ...
- 411
2
votes
0
answers
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Isometry embedding
Problem:
Let $(M,g)$ be a compact Riemannian manifold. Then clearly $(M,d_R)$ is a metric space, where $$ d_R(x,y)=\|x-y\| \quad \forall x,y\in M $$
Now let's see the following:
1. The Kuratowski ...
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