Length and Area Functions on Groups and Quasi-Isometric Higman Embeddings

TL;DR

This paper surveys recent developments in the study of asymptotic functions of groups, focusing on length and area functions, and discusses the methods used in proving these results.

Contribution

It provides a comprehensive overview of recent results on asymptotic functions and introduces the proof techniques employed in this area.

Findings

Summary of recent results on asymptotic functions

Discussion of proof methods used in the field

Connections to quasi-isometric Higman embeddings

Abstract

We survey recent results about asymptotic functions of groups, obtained by the authors in collaboration with J.-C.Birget, V. Guba and E. Rips. We also discuss methods used in the proofs of these results.