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


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 map Alexandrov-Fenchel inequalies. 


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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

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