Classification of fractional, singular Yamabe metrics on a twice punctured sphere I
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866914184522891264 |
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| author | Andrade, João Henrique DelaTorre, Azahara Ò, João Marcos do Ratzkin, Jesse Wei, Juncheng |
| author_facet | Andrade, João Henrique DelaTorre, Azahara Ò, João Marcos do Ratzkin, Jesse Wei, Juncheng |
| contents | The Delaunay metrics form a family of conformally flat, constant fractional Q-curvature metrics on a twice-punctured sphere. They are all (after a Möbius 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2511_05225 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Classification of fractional, singular Yamabe metrics on a twice punctured sphere I Andrade, João Henrique DelaTorre, Azahara Ò, João Marcos do Ratzkin, Jesse Wei, Juncheng Differential Geometry Analysis of PDEs 35J60, 35R11, 53C21, 53A30, 35B33, 35B40 The Delaunay metrics form a family of conformally flat, constant fractional Q-curvature metrics on a twice-punctured sphere. They are all (after a Möbius 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. |
| title | Classification of fractional, singular Yamabe metrics on a twice punctured sphere I |
| topic | Differential Geometry Analysis of PDEs 35J60, 35R11, 53C21, 53A30, 35B33, 35B40 |
| url | https://arxiv.org/abs/2511.05225 |