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Computations of the orbifold Yamabe invariant

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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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Authors and Affiliations

  1. Division of Mathematics, Graduate School of Information Sciences, Tohoku University, Sendai, 980-8579, Japan

    Kazuo Akutagawa

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  1. Kazuo Akutagawa
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Correspondence to Kazuo Akutagawa.

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Supported in part by the Grants-in-Aid for Scientific Research (C), Japan Society for the Promotion of Science, No. 21540097.

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Akutagawa, K. Computations of the orbifold Yamabe invariant. Math. Z. 271, 611–625 (2012). https://doi.org/10.1007/s00209-011-0880-0

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