Minimal Disc Diagrams of 5 / 9 -Simplicial Complexes

Abstract

We introduce and study a local combinatorial condition, called the $5/9$-condition, on a simplicial complex, implying Gromov hyperbolicity of its universal cover. We hereby give an application of another combinatorial condition, called $8$-location, introduced by Damian Osajda. Along the way we prove the minimal filling diagrams lemma for $5/9$-complexes.