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Conformally prescribed scalar curvature on orbifolds

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arxiv 2112.05207 v1 pith:DFTVXQQZ submitted 2021-12-09 math.DG math.AP

Tao Ju , Jeff Viaclovsky This is my paper · ORCID
classification math.DGmath.AP
keywords orbifoldstheoremcurvatureprescribedproblemscalarcaseclass
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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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