Computations of the orbifold Yamabe invariant

2010/09/18 by Akutagawa, Kazuo · 1 citation
#Differential Geometry (math.DG) #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.1009.3576

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.

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