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arXiv · 2511.05225

Classification of fractional, singular Yamabe metrics on a twice punctured sphere I

João Henrique Andrade·Azahara DelaTorre·João Marcos do Ò·Jesse Ratzkin·Juncheng Wei
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Abstract

The Delaunay metrics form a family of conformally flat, constant fractional Q-curvature metrics on a twice-punctured sphere. They are all (after a M\"obius transformation) rotationally symmetric and periodic, and admit several elegant variational descriptions. We prove that, when s is close to but less than 1, any complete, conformally flat constant Q-curvature metric on a twice-punctured sphere is a Delaunay metric. Along the way, we prove a sharp a priori bound for the conformal factor of these metrics, which may be of independent interest.

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João Henrique Andrade, Azahara DelaTorre, João Marcos do Ò, Jesse Ratzkin, Juncheng Wei. 2025-11-07. Classification of fractional, singular Yamabe metrics on a twice punctured sphere I. https://arxiv.org/abs/2511.05225

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