Triangulating metric surfaces

TL;DR

This paper proves that any surface-like metric space can be divided into small convex triangles, extending previous results to more general surfaces without curvature restrictions.

Contribution

It generalizes the Alexandrov--Zalgaller decomposition theorem to all length metric surfaces, regardless of curvature bounds.

Findings

Decomposition of metric surfaces into convex triangles of arbitrarily small diameter

Extension of Alexandrov--Zalgaller result to more general surfaces

Supports further geometric analysis of metric surfaces

Abstract

We prove that any length metric space homeomorphic to a surface may be decomposed into non-overlapping convex triangles of arbitrarily small diameter. This generalizes a previous result of Alexandrov--Zalgaller for surfaces of bounded curvature.