Abstract
Loomis and Whitney proved an inequality between volume and areas of projections of an open set in n-dimensional space related to the isoperimetric inequality. They reduced the problem to a combinatorial theorem proved by a repeated use of Hölder inequality. In this paper we prove a general inequality between real numbers which easily implies the combinatorial theorem of Loomis and Whitney.
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Reference
L. H. Loomis and H. Whitney, An inequality related to the isoperimetric inequality, Bull. Amer. Math. Soc., 55 (1949), 961–962.
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Wiśniowska-Wajnryb, A. An elementary proof of the Loomis–Whitney theorem. Acta Math. Hungar. 164, 518–521 (2021). https://doi.org/10.1007/s10474-021-01162-6
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DOI: https://doi.org/10.1007/s10474-021-01162-6