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arXiv · 2402.10297

Spinorial Yamabe-type equations and the B\"ar-Hijazi-Lott invariant

Jurgen Julio-Batalla
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Abstract

We consider on a closed Riemannian spin manifold $(M^n,g,\sigma)$ the spinorial Yamabe type equation $D_g\varphi=\lambda|\varphi|^{\frac{2}{n-1}}\varphi$, where $\varphi$ is a spinor field and $\lambda$ is a positive constant. For a normalized solution $\varphi$ of this equation we find a positive lower bound for $\lambda^2$. As an application we obtain an explicit lower bound of the B\"ar-Hijazi-Lott invariant for some spin manifolds with positive scalar curvature.

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Jurgen Julio-Batalla. 2024-02-15. Spinorial Yamabe-type equations and the B\"ar-Hijazi-Lott invariant. https://arxiv.org/abs/2402.10297

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