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arXiv · 2112.05207

Conformally prescribed scalar curvature on orbifolds

Tao Ju·Jeff Viaclovsky
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Abstract

We study the prescribed scalar curvature problem in a conformal class on orbifolds with isolated singularities. We prove a compactness theorem in dimension $4$, and an existence theorem which holds in dimensions $n \geq 4$. This problem is more subtle than the manifold case since the positive mass theorem does not hold for ALE metrics in general. We also determine the $\rm{U}(2)$-invariant Leray-Schauder degree for a family of negative-mass orbifolds found by LeBrun.

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Tao Ju, Jeff Viaclovsky. 2021-12-09. Conformally prescribed scalar curvature on orbifolds. https://doi.org/10.1007/s00220-022-04542-3

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