Optimal Transport and Tessellation
نویسنده
چکیده
Optimal transport from the volume measure to a convex combination of Dirac measures yields a tessellation of a Riemannian manifold into pieces of arbitrary relative size. This tessellation is studied for the cost functions cp(z, y) = 1 p d(z, y) and 1 ≤ p < ∞. Geometric descriptions of the tessellations for all p is obtained for compact subsets of the Euclidean space and the sphere. For p = 1 this approach yields Laguerre tessellations for all compact Riemannian manifolds.
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