@article{96f75eb8f588432d89322335049d9290,
title = "A Remarkable Measure Preserving Diffeomorphism between Two Convex Bodies in ℝn",
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.",
keywords = "Alexandrov-Fenchel inequalities, Brenier map",
author = "S. Alesker and S. Dar and V. Milman",
note = "Funding Information: ★ Partially supported by a Minkowski Center grant. ★★ Research partially supported by the Israel Science Sciences and Humanities.",
year = "1999",
doi = "10.1023/A:1005087216335",
language = "אנגלית",
volume = "74",
pages = "201--212",
journal = "Geometriae Dedicata",
issn = "0046-5755",
publisher = "Springer Netherlands",
number = "2",
}