Gap Phenomenon for Yamabe Type Problems of $M^m\times T^{n-m}$
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2026
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| Acceso en línea: | |
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| _version_ | 1866916043379703808 |
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| author | Wang, Fang Wang, Zhixin |
| author_facet | Wang, Fang Wang, Zhixin |
| contents | We prove that if $(M^m, h)$ is a Yamabe metric, then the product metric $h + g_{\mathrm{flat}}$ on $M^m \times T^{n-m}$ is also a Yamabe metric whenever the flat torus $T^{n-m}$ is sufficiently small. This generalizes earlier results for $S^1 \times S^{n-1}$. Our method extends to the study of Type~I and Type~II Yamabe constants, $Q$-curvature problems, and an isoperimetric-ratio type problem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_25145 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Gap Phenomenon for Yamabe Type Problems of $M^m\times T^{n-m}$ Wang, Fang Wang, Zhixin Differential Geometry We prove that if $(M^m, h)$ is a Yamabe metric, then the product metric $h + g_{\mathrm{flat}}$ on $M^m \times T^{n-m}$ is also a Yamabe metric whenever the flat torus $T^{n-m}$ is sufficiently small. This generalizes earlier results for $S^1 \times S^{n-1}$. Our method extends to the study of Type~I and Type~II Yamabe constants, $Q$-curvature problems, and an isoperimetric-ratio type problem. |
| title | Gap Phenomenon for Yamabe Type Problems of $M^m\times T^{n-m}$ |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2605.25145 |