Slicing Convex Sets and Measures by a Hyperplane

  • Authors:

  • Imre Bárány;Alfredo Hubard;Jesús Jerónimo

  • Affiliations:

  • Hungarian Academy of Sciences, Rényi Institute of Mathematics, P.O. Box 127, 1364, Budapest, Hungary and University College London, Department of Mathematics Gower Street, London, WC1E 6BT, ...;Ciudad Universitaria, Instituto de Matemáticas, UNAM, P.O. Box 127, D.F. 04510, Mexico, Mexico;Centro de Investigación en Matemáticas A.C., P.O. Box 127, Apdo. Postal 402, D.F. 04510, Guanajuato, Mexico

  • Venue:
  • Discrete & Computational Geometry
  • Year:
  • 2008

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Abstract

Given convex bodies K1,…,Kd in ℝd and numbers α1,…,αd∈[0,1], we give a sufficient condition for existence and uniqueness of an (oriented) halfspace H with Vol (H∩Ki)=αi⋅Vol Ki for every i. The result is extended from convex bodies to measures.