Web12 de jun. de 2024 · Loomis and Whitney proved an inequality between volume and areas of projections of an open set in n-dimensional space related to the isoperimetric … Webfrom the Loomis–Whitney inequality, proven in [LW]. To state their result, we need a little notation. Let π j: Rn → Rn−1 be the linear map that forgets the jth coordinate: π j(x 1,...,x …
On the Reverse Loomis–Whitney Inequality - Semantic Scholar
WebA proof of a Loomis-Whitney type inequality via optimal transport (2024) J. Math. Anal. Appl. 471 (2024), no. 1-2, 489-495. The Loomis-Whitney inequality is one of the most … Web1 de abr. de 2016 · The Loomis–Whitney inequality is one of the fundamental inequalities in convex geometry and has been studied intensively; see e.g., [3], [6], [7], [8], [9], [10], … bdo mediah
ON THE LOOMIS-WHITNEY INEQUALITY FOR ISOTROPIC …
WebThe generalized Loomis-Whitney inequality for (probability) measures especially allows some interesting applications in Sec-tion 3. For example, for various distribution … WebThe dual Loomis–Whitney inequality for isotropic measures is proved in Section 4. In the final section, we focus on the dual Loomis–Whitney inequality for two important isotropic measures, namely the spherical Lebesgue measure and the cross measure. 2. Notations and preliminaries In mathematics, the Loomis–Whitney inequality is a result in geometry, which in its simplest form, allows one to estimate the "size" of a $${\displaystyle d}$$-dimensional set by the sizes of its $${\displaystyle (d-1)}$$-dimensional projections. The inequality has applications in incidence geometry, the study of so-called … Ver mais The Loomis–Whitney inequality can be used to relate the Lebesgue measure of a subset of Euclidean space $${\displaystyle \mathbb {R} ^{d}}$$ to its "average widths" in the coordinate directions. This is in fact the original version … Ver mais • Alon, Noga; Spencer, Joel H. (2016). The probabilistic method. Wiley Series in Discrete Mathematics and Optimization (Fourth edition of 1992 original ed.). Hoboken, NJ: Ver mais The Loomis–Whitney inequality is a special case of the Brascamp–Lieb inequality, in which the projections πj above are replaced by more general linear maps, … Ver mais bdo mediah adventure journal 3