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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2603.23218 |
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Table of Contents:
- This paper is concerned with the zero mode equation $D_gφ=iA\cdotφ$ on closed spin manifold $(M^n,g,σ)$ of positive scalar curvature. Here $A$ is a real one form on $M$. We proved that if $(φ, A)$ is a non trivial solution of the zero mode equation then $$\parallel dA\parallel_{n/2}>Y(M^n,[g])/(4v_n^{1/2}),$$ where $Y(M^n,[g])$ is the Yamabe constant of $(M^n,g)$ and $v_n=\left[\frac{n}{2}\right]$. In the case of the round sphere $(\mathbb{S}^n,g_{can},σ_{can})$ this result confirms that the inequality obtained in \cite{Frank} is not sharp.