Maximal $\Lambda(p)$-subsets of manifolds

TL;DR

This paper constructs maximal bbb1(p)b2-subsets on various curved manifolds using advanced restriction, decoupling, and probabilistic techniques, achieving optimal Lebesgue exponent ranges.

Contribution

It introduces a novel method for constructing maximal bbb1(p)b2-subsets on curved manifolds within optimal Lebesgue exponent ranges.

Findings

Successful construction of maximal bbb1(p)b2-subsets on curved manifolds.

Integration of restriction estimates, decoupling, and probabilistic methods.

Achievement of optimal Lebesgue exponent ranges.

Abstract

We construct maximal $\Lambda(p)$-subsets on a large class of curved manifolds, in an optimal range of Lebesgue exponents $p$. Our arguments combine restriction estimates and decoupling with old and new probabilistic estimates.