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One more proof of the Alexandrov–Fenchel inequality
Dario Cordero–Erausquina b, Bo’az Klartagc d, Quentin Mérigote f, Filippo Santambrogiog h
- aInstitut de mathématiques de Jussieu , Sorbonne Université , 4 , place Jussieu , 75252 Paris cedex 05 , France
- bIMJ - Institut de Mathématiques de Jussieu (2, place Jussieu 75251 Paris Cedex 05 - France)
- cDepartment of Mathematics , Weizmann Institute of Science , Rehovot 76100 , Israel
- dWeizmann Institute of Science - Department of Mathematics (Faculty of Mathematics and Computer Science The Weizmann Institute of Science 234 Herzl Street,Rehovot 76100, Israel - Israel)
- eLaboratoire de mathématiques d'Orsay , Universié Paris-Sud , CNRS , Université Paris-Saclay , 91405 Orsay , France
- fLM-Orsay - Laboratoire de Mathématiques d'Orsay (France)
- gInstitut Camille-Jordan , Université Claude-Bernard -Lyon -1 , 43, boulevard du 11-Novembre-1918 , 69622 Villeurbanne cedex , France
- hICJ - Institut Camille Jordan (Bât. Jean Braconnier 43 bd du 11 novembre 1918 69622 VILLEURBANNE CEDEX - France)
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Abstract
We present a short proof of the Alexandrov–Fenchel inequalities, which mixes elementary algebraic properties and convexity properties of mixed volumes of polytopes.