A Remark on the Rigidity of Delaunay Triangulated Plane

TL;DR

This paper improves the understanding of the rigidity of Delaunay triangulated planes by weakening the conditions needed for rigidity from uniformly acute to uniformly Delaunay, enhancing theoretical insights in discrete conformality.

Contribution

It extends Wu's previous rigidity result by replacing the uniformly acute condition with a weaker uniformly Delaunay condition in the context of geodesic triangulated planes.

Findings

Rigidity holds under the uniformly Delaunay condition

The proof modifies Wu's original approach

Broader applicability of rigidity results in discrete conformality

Abstract

In \cite{Wu22}, under the uniformly acute condition, Wu showed the rigidity of the geodesic triangulated plane under Luo's discrete conformality. In this article, by modifying Wu's proof, we improve this result by weakening the uniformly acute condition to the uniformly Delaunay condition.