Lifting Methods in Mass Partition Problems

  title={Lifting Methods in Mass Partition Problems},
  author={Pablo Sober'on and Yuki Takahashi},
  journal={International Mathematics Research Notices},
Many results about mass partitions are proved by lifting $\mathds {R}^d$ to a higher-dimensional space and dividing the higher-dimensional space into pieces. We extend such methods to use lifting arguments to polyhedral surfaces. Among other results, we prove the existence of equipartitions of $d+1$ measures in $\mathds {R}^d$ by parallel hyperplanes and of $d+2$ measures in $\mathds {R}^d$ by concentric spheres. For measures whose supports are sufficiently well separated, we prove results… 
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