Abstract: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.
| Subjects: | Differential Geometry (math.DG) |
| Cite as: | arXiv:2605.25145 [math.DG] |
| (or arXiv:2605.25145v1 [math.DG] for this version) | |
| https://doi.org/10.48550/arXiv.2605.25145 arXiv-issued DOI via DataCite (pending registration) |
From: Zhixin Wang [view email]
[v1]
Sun, 24 May 2026 15:54:29 UTC (27 KB)
此内容由惯性聚合(RSS阅读器)自动聚合整理，仅供阅读参考。 原文来自 — 版权归原作者所有。