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arXiv · 2605.25145

Gap Phenomenon for Yamabe Type Problems of $M^m\times T^{n-m}$

Fang Wang·Zhixin Wang
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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.

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Fang Wang, Zhixin Wang. 2026-05-24. Gap Phenomenon for Yamabe Type Problems of $M^m\times T^{n-m}$. https://arxiv.org/abs/2605.25145

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