Concept

Loomis–Whitney inequality

Summary
In mathematics, the Loomis–Whitney inequality is a result in geometry, which in its simplest form, allows one to estimate the "size" of a d-dimensional set by the sizes of its (d-1)-dimensional projections. The inequality has applications in incidence geometry, the study of so-called "lattice animals", and other areas. The result is named after the American mathematicians Lynn Harold Loomis and Hassler Whitney, and was published in 1949. Statement of the inequality Fix a dimension d\ge 2 and consider the projections :\pi_{j} : \mathbb{R}^{d} \to \mathbb{R}^{d - 1}, :\pi_{j} : x = (x_{1}, \dots, x_{d}) \mapsto \hat{x}{j} = (x{1}, \dots, x_{j - 1}, x_{j + 1}, \dots, x_{d}). For each 1 ≤ j ≤ d, let :g_{j} : \mathbb{R}^{d - 1} \to [0, + \infty), :g_{j} \in L^{d - 1} (\mathbb{R}^{d -1}). Then the Loomis–Whitney inequality holds: :\left|\prod_{j=1}^d g_j \circ \pi_j\right|_{L^
About this result
This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.
Related publications

Loading

Related people

Loading

Related units

Loading

Related concepts

Loading

Related courses

Loading

Related lectures

Loading