Optimal Transport and Tessellation TeX Export

@article{citeulike:5371296, abstract = {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 and the sphere. For \$p=1\$ this approach yields Laguerre tessellations for all compact Riemannian manifolds.}, archivePrefix = {arXiv}, author = {Huesmann, Martin}, citeulike-article-id = {5371296}, citeulike-linkout-0 = {http://arxiv.org/abs/0908.0442}, citeulike-linkout-1 = {http://arxiv.org/pdf/0908.0442}, day = {4}, eprint = {0908.0442}, keywords = {regularity, riemannian-manifold, tesselation, transport}, month = {Aug}, posted-at = {2009-08-05 12:21:46}, priority = {2}, title = {Optimal Transport and Tessellation}, url = {http://arxiv.org/abs/0908.0442}, year = {2009} }

TY - JOUR ID - citeulike:5371296 L3 - citeulike-article-id:5371296 N2 - 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 and the sphere. For $p=1$ this approach yields Laguerre tessellations for all compact Riemannian manifolds. TI - Optimal Transport and Tessellation KW - regularity KW - riemannian-manifold KW - tesselation KW - transport AU - Huesmann, Martin PY - 2009/Aug/04/ UR - http://arxiv.org/abs/0908.0442 ER -