Weyl energy and connected sums of four-manifolds
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866918032051273728 |
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| author | Malchiodi, Andrea Malizia, Francesco |
| author_facet | Malchiodi, Andrea Malizia, Francesco |
| contents | Given two closed, oriented Riemannian four-manifolds $(M,g_M)$ and $(Z,g_Z)$, which are not locally conformally flat and not both self-dual or both anti-self-dual, we prove that there exists a metric $g_Y$ on the connected sum $Y\cong M\#Z$ such that the Weyl energy of $g_Y$ is strictly smaller than the sum of Weyl energies of $g_M$ and $g_Z$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_17752 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Weyl energy and connected sums of four-manifolds Malchiodi, Andrea Malizia, Francesco Differential Geometry 53C21, 58E11, 49J99 Given two closed, oriented Riemannian four-manifolds $(M,g_M)$ and $(Z,g_Z)$, which are not locally conformally flat and not both self-dual or both anti-self-dual, we prove that there exists a metric $g_Y$ on the connected sum $Y\cong M\#Z$ such that the Weyl energy of $g_Y$ is strictly smaller than the sum of Weyl energies of $g_M$ and $g_Z$. |
| title | Weyl energy and connected sums of four-manifolds |
| topic | Differential Geometry 53C21, 58E11, 49J99 |
| url | https://arxiv.org/abs/2505.17752 |