Planar doubling nodal solutions to the Yamabe equation with maximal rank
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866917382860046336 |
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| author | Li, Yuanli Sun, Liming |
| author_facet | Li, Yuanli Sun, Liming |
| contents | This article constructs two families of nodal solutions to the Yamabe equation, each concentrating along two planar circles. One family is conformally equivalent to the one previously obtained by Medina--Musso. The second family is a twisted variant of the first; it is new and is derived from ansatzes that are not Kelvin invariant, in contrast to a standard assumption in earlier works. In addition, in dimension 3, these solutions attain maximal rank. By means of a continuous family of conformal transformations, we then analyze the interaction of the two circles, which display a crossing phenomenon reminiscent, in some sense, of leap-frogging behavior in vortex dynamics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_02978 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Planar doubling nodal solutions to the Yamabe equation with maximal rank Li, Yuanli Sun, Liming Analysis of PDEs This article constructs two families of nodal solutions to the Yamabe equation, each concentrating along two planar circles. One family is conformally equivalent to the one previously obtained by Medina--Musso. The second family is a twisted variant of the first; it is new and is derived from ansatzes that are not Kelvin invariant, in contrast to a standard assumption in earlier works. In addition, in dimension 3, these solutions attain maximal rank. By means of a continuous family of conformal transformations, we then analyze the interaction of the two circles, which display a crossing phenomenon reminiscent, in some sense, of leap-frogging behavior in vortex dynamics. |
| title | Planar doubling nodal solutions to the Yamabe equation with maximal rank |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2604.02978 |