A note on arclength null quadrature domains

TL;DR

This paper proves the existence of a roof function for arclength null quadrature domains with finitely many boundary components, advancing their classification by removing previous assumptions.

Contribution

It establishes the existence of a roof function for these domains, filling a gap in their mathematical classification.

Findings

Existence of roof function for arclength null quadrature domains

Bridging gap in classification of these domains

Removes previous a priori assumptions

Abstract

We prove the existence of a roof function for arclength null quadrature domains having finitely many boundary components. This bridges a gap toward classification of arclength null quadrature domains by removing an a priori assumption from previous classification results.