Advertisement

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

Convex Body Equality Sign Equality Case Parallel Translation Elementary Inequality 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

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

Personalised recommendations