Average distortion embeddings, nonlinear spectral gaps, and a metric John theorem (after Assaf Naor)

TL;DR

This paper surveys the theory of nonlinear spectral gaps, providing a comprehensive overview and a self-contained proof of Naor's average John theorem, highlighting recent advances in metric embedding theory.

Contribution

It offers a detailed survey and a new self-contained proof of Naor's average John theorem, advancing understanding of nonlinear spectral gaps.

Findings

Self-contained proof of Naor's average John theorem

Enhanced understanding of nonlinear spectral gaps

Connections between spectral gaps and metric embeddings

Abstract

We survey various aspects of the theory of nonlinear spectral gaps. In particular, we present a self-contained proof of Naor's average John theorem.