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Creators/Authors contains: "Takahashi, Yuki"

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  1. ; (, International Mathematics Research Notices)
    Abstract 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 where one can cut a fixed (possibly different) fraction of each measure either by parallel hyperplanes, concentric spheres, convex polyhedral surfaces of few facets, or convex polytopes with few vertices. 
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  2. ; ; ; (, International journal of mathematics and computer science)
    Accepted Manuscript Full Text Available
  3. ; ; ; ; ; (, International journal of mathematics and computer science)
    Accepted Manuscript Full Text Available