Min-max theory and Yamabe metrics on conical four-manifolds
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866912519011958784 |
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| author | Freguglia, Mattia Malchiodi, Andrea Malizia, Francesco |
| author_facet | Freguglia, Mattia Malchiodi, Andrea Malizia, Francesco |
| contents | We prove existence of Yamabe metrics on four-manifolds possessing finitely-many conical points with $\mathbb{Z}_2$-group, using for the first time a min-max scheme in the singular setting. In our variational argument we need to deform continuously regular bubbles into singular ones, while keeping the Yamabe energy sufficiently low. For doing this, we exploit recent positive mass theorems in the conical setting and study how the mass of the conformal blow-up diverges as the blow-up point approaches the singular set. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_02667 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Min-max theory and Yamabe metrics on conical four-manifolds Freguglia, Mattia Malchiodi, Andrea Malizia, Francesco Differential Geometry Analysis of PDEs 53C18, 53C21, 58J60, 35J20 We prove existence of Yamabe metrics on four-manifolds possessing finitely-many conical points with $\mathbb{Z}_2$-group, using for the first time a min-max scheme in the singular setting. In our variational argument we need to deform continuously regular bubbles into singular ones, while keeping the Yamabe energy sufficiently low. For doing this, we exploit recent positive mass theorems in the conical setting and study how the mass of the conformal blow-up diverges as the blow-up point approaches the singular set. |
| title | Min-max theory and Yamabe metrics on conical four-manifolds |
| topic | Differential Geometry Analysis of PDEs 53C18, 53C21, 58J60, 35J20 |
| url | https://arxiv.org/abs/2508.02667 |