Conformal metrics of constant scalar curvature with unbounded volumes
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866916811868471296 |
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| author | Gong, Liuwei Li, Yanyan |
| author_facet | Gong, Liuwei Li, Yanyan |
| contents | For $n\geq 25$, we construct a smooth metric $\tilde{g}$ on the standard $n$-dimensional sphere $\mathbb{S}^n$ such that there exists a sequence of smooth metrics $\{\tilde{g}_k\}_{k\in\mathbb{N}}$ conformal to $\tilde g$ where each $\tilde g_k$ has scalar curvature $R_{\tilde{g}_k}\equiv 1$ and their volumes $\text{Vol}(\mathbb{S}^n,\tilde{g}_k)$ tend to infinity as $k$ approaches infinity. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2406_06898 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Conformal metrics of constant scalar curvature with unbounded volumes Gong, Liuwei Li, Yanyan Analysis of PDEs Differential Geometry For $n\geq 25$, we construct a smooth metric $\tilde{g}$ on the standard $n$-dimensional sphere $\mathbb{S}^n$ such that there exists a sequence of smooth metrics $\{\tilde{g}_k\}_{k\in\mathbb{N}}$ conformal to $\tilde g$ where each $\tilde g_k$ has scalar curvature $R_{\tilde{g}_k}\equiv 1$ and their volumes $\text{Vol}(\mathbb{S}^n,\tilde{g}_k)$ tend to infinity as $k$ approaches infinity. |
| title | Conformal metrics of constant scalar curvature with unbounded volumes |
| topic | Analysis of PDEs Differential Geometry |
| url | https://arxiv.org/abs/2406.06898 |