Small eigenvalues of surfaces - old and new

TL;DR

This paper explores small eigenvalues of surfaces, reviewing classical results and introducing new ideas from recent research to deepen understanding of their properties and significance.

Contribution

It extends classical work on small eigenvalues and incorporates novel ideas from recent studies, advancing the theoretical understanding of eigenvalues in surface geometry.

Findings

Extended classical results of Buser and Randol

Introduced new methods from Sévennec, Otal, and Otal-Rosas

Enhanced understanding of small eigenvalues in surface theory

Abstract

We discuss our recent work on small eigenvalues of surfaces. As an introduction, we present and extend some of the by now classical work of Buser and Randol and explain novel ideas from articles of S\'evennec, Otal, and Otal-Rosas which are of importance in our line of thought.