A Remarkable Measure Preserving Diffeomorphism between Two Convex Bodies in ℝn

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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.

Original languageEnglish
Pages (from-to)201-212
Number of pages12
JournalGeometriae Dedicata
Volume74
Issue number2
DOIs
StatePublished - 1999

Keywords

  • Alexandrov-Fenchel inequalities
  • Brenier map

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