Computations of the orbifold Yamabe invariant

Details Computations of the orbifold Yamabe invariant Computations of the orbifold Yamabe invariant

2010-09-18

arxiv.org/abs/1009.3576v1

Mathematics

Differential Geometry

14 pages, 3 figures

Scientific paper

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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