Sharp Estimates for some Integral-Geometric Quantities Related To Transversality, Curvature And Visibility

TL;DR

This paper derives precise bounds for integral-geometric quantities related to transversality, curvature, and visibility, with applications in harmonic analysis and geometric measure theory.

Contribution

It provides new exact bounds for these quantities using convex geometric inequalities, advancing understanding in harmonic analysis and geometric measure theory.

Findings

Derived exact lower and upper bounds for integral-geometric quantities

Connected geometric inequalities to harmonic analysis applications

Enhanced understanding of transversality and visibility measures

Abstract

We investigate integral-geometric quantities arising from harmonic analysis which measure visibility and transversality. Motivated by their applications in multilinear Kakeya problems and affine-invariant measures on surfaces, we derive exact lower and upper bounds employing geometric and functional inequalities of convex geometry.