Spinorial Yamabe-type equations and the Bär-Hijazi-Lott invariant
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866909108776468480 |
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| author | Julio-Batalla, Jurgen |
| author_facet | Julio-Batalla, Jurgen |
| contents | We consider on a closed Riemannian spin manifold $(M^n,g,σ)$ the spinorial Yamabe type equation $D_gφ=λ|φ|^{\frac{2}{n-1}}φ$, where $φ$ is a spinor field and $λ$ is a positive constant. For a normalized solution $φ$ of this equation we find a positive lower bound for $λ^2$. As an application we obtain an explicit lower bound of the Bär-Hijazi-Lott invariant for some spin manifolds with positive scalar curvature. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_10297 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Spinorial Yamabe-type equations and the Bär-Hijazi-Lott invariant Julio-Batalla, Jurgen Differential Geometry Analysis of PDEs We consider on a closed Riemannian spin manifold $(M^n,g,σ)$ the spinorial Yamabe type equation $D_gφ=λ|φ|^{\frac{2}{n-1}}φ$, where $φ$ is a spinor field and $λ$ is a positive constant. For a normalized solution $φ$ of this equation we find a positive lower bound for $λ^2$. As an application we obtain an explicit lower bound of the Bär-Hijazi-Lott invariant for some spin manifolds with positive scalar curvature. |
| title | Spinorial Yamabe-type equations and the Bär-Hijazi-Lott invariant |
| topic | Differential Geometry Analysis of PDEs |
| url | https://arxiv.org/abs/2402.10297 |