Geometriae Dedicata

, Volume 74, Issue 2, pp 201–212

A Remarkable Measure Preserving Diffeomorphism between two Convex Bodies in ℝn

  • S. Alesker
  • S. Dar
  • V. Milman
Article

DOI: 10.1023/A:1005087216335

Cite this article as:
Alesker, S., Dar, S. & Milman, V. Geometriae Dedicata (1999) 74: 201. doi:10.1023/A:1005087216335

Abstract

We prove that for any two convex open bounded bodies K and T there exists a diffeomorphism f : K → T preserving volume ratio (i.e. with constant determinant of the Jacobian) and such that the Minkowski sum K + T { x + f (x) | x ∈ K }. As an application of this method, we prove some of the Alexandov–Fenchel inequalities.

Brenier mapAlexandrov-Fenchel inequalies.

Copyright information

© Kluwer Academic Publishers 1999

Authors and Affiliations

  • S. Alesker
    • 1
  • S. Dar
    • 1
  • V. Milman
    • 1
  1. 1.Department of MathematicsTel-Aviv UniversityTel-AvivIsrael