• Corpus ID: 16927657

Optimal Transport and Tessellation

@article{Huesmann2009OptimalTA,
  title={Optimal Transport and Tessellation},
  author={Martin Huesmann},
  journal={arXiv: Probability},
  year={2009}
}
  • M. Huesmann
  • Published 4 August 2009
  • Mathematics
  • arXiv: Probability
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 $c_p(z,y)=\frac{1}{p}d^p(z,y)$ and $1\leq p<\infty$. Geometric descriptions of the tessellations for all $p$ is obtained for compact subsets of the Euclidean space. For $p=2$ this approach yields Laguerre tessellations. For $p=1$ it induces Johnson Mehl diagrams for all… 

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  • 2009