Computations of the orbifold Yamabe invariant

TL;DR

This paper investigates the orbifold Yamabe invariant, establishing inequalities, conditions for equality, and solving the orbifold Yamabe problem to compute the invariant for specific compact orbifolds.

Contribution

It introduces a fundamental inequality for the orbifold Yamabe invariant, provides conditions for equality, and solves the orbifold Yamabe problem under certain conditions.

Findings

Established an upper bound for the orbifold Yamabe invariant.

Provided criteria for the non-positivity of the invariant.

Computed exact values of the invariant for specific orbifolds.

Abstract

We consider the Yamabe invariant of a compact orbifold with finitely many singular points. We prove a fundamental inequality for the estimate of the invariant from above, which also includes a criterion for the non-positivity of it. Moreover, we give a sufficient condition for the equality in the inequality. In order to prove it, we also solve the orbifold Yamabe problem under a certain condition. We use these results to give some exact computations of the Yamabe invariant of compact orbifolds.