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arXiv · 2503.09234

An end to end gluing construction for metrics of constant Q-curvature

A. Sophie Aiken·Rayssa Caju·Jesse Ratzkin·Almir Silva Santos
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Abstract

We produce many new complete, constant Q-curvature metrics on finitely punctured spheres by gluing together known examples. In our construction we truncate one end of each summand and glue the two summands together "end-to-end," where we've truncated them. We use this construction to show that the unmarked moduli space of solutions with a fixed number of punctures is topologically nontrivial provided the number of punctures is at least four.

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A. Sophie Aiken, Rayssa Caju, Jesse Ratzkin, Almir Silva Santos. 2025-03-12. An end to end gluing construction for metrics of constant Q-curvature. https://arxiv.org/abs/2503.09234

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