Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

A short proof of the multilinear Kakeya inequality

Larry Guth

Abstract

We give a short proof of a slightly weaker version of the multilinear Kakeya inequality proven by Bennett, Carbery, and Tao.

A short proof of the multilinear Kakeya inequality

Abstract

We give a short proof of a slightly weaker version of the multilinear Kakeya inequality proven by Bennett, Carbery, and Tao.

Paper Structure

This paper contains 6 sections, 7 theorems, 25 equations.

Table of Contents

  1. The proof of the multilinear Kakeya inequality
  2. Reduction to nearly axis parallel tubes
  3. The axis parallel case (Loomis-Whitney)
  4. The multiscale argument
  5. Some small generalizations
  6. On Lipschitz curves

Key Result

Theorem 1

Suppose that $l_{j,a}$ are lines in $\mathbb{R}^n$, and that each line $l_{j,a}$ makes an angle of at most $(10 n)^{-1}$ with the $x_j$-axis. Let $Q_S$ denote any cube of side length $S$. Then for any $\epsilon > 0$ and any $S \ge 1$, the following integral inequality holds:

Theorems & Definitions (10)

  • Theorem 1
  • Theorem 2
  • Theorem 3
  • Lemma 4
  • proof
  • Corollary 5
  • proof
  • Corollary 6
  • proof
  • Theorem 7