The Brunn-Minkowski Inequality and the Classical Isoperimetric Inequality

  • Yuriĭ Dmitrievich Burago
  • Viktor Abramovich Zalgaller
Chapter
Part of the Grundlehren der mathematischen Wissenschaften book series (GL, volume 285)

Abstract

To every pair of non-empty sets A, B ⊂ ℝ n their (vector) Minkowski sum is defined by A + B = {a + b: aA, bB}. If A, B are compact sets (i.e. bounded closed sets), then A + B is compact. In this case each of the sets A, B, A + B necessarily has a volume (its Lebesgue measure). Denote these volumes by V(A), V(B), V(A + B).

Keywords

Manifold Hull BarB 

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Copyright information

© Springer-Verlag Berlin Heidelberg 1988

Authors and Affiliations

  • Yuriĭ Dmitrievich Burago
    • 1
  • Viktor Abramovich Zalgaller
    • 1
  1. 1.Leningrad Branch of the Steklov Mathematical InstituteLeningradUSSR

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