Corpus ID: 118850026

Equipartition of several measures

@article{Karasev2010EquipartitionOS,
  title={Equipartition of several measures},
  author={R. Karasev},
  journal={arXiv: Metric Geometry},
  year={2010}
}
  • R. Karasev
  • Published 2010
  • Mathematics
  • arXiv: Metric Geometry
  • We prove several results of the following type: any $d$ measures in $\mathbb R^d$ can be partitioned simultaneously into $k$ equal parts by a convex partition (this particular result is proved independently by Pablo Sober\'on). Another example is: Any convex body in the plane can be partitioned into $q$ parts of equal areas and perimeters provided $q$ is a prime power. The above results give a partial answer to several questions posed by A. Kaneko, M. Kano, R. Nandakumar, N. Ramana Rao, and I… CONTINUE READING
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