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arXiv · 2510.17780

On fill-ins with scalar curvature bounded from below and an inequality of Hijazi-Montiel-Rold\'an

Simon Brendle·Raphael Tsiamis·Yipeng Wang
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Abstract

We consider fill-ins of spin manifolds with scalar curvature bounded by $-n(n-1)$. Gromov proposed a conjecture relating the infimum of the mean curvature of such a fill-in to the hyperspherical radius. We observe that the inequality conjectured by Gromov follows by combining an inequality of Hijazi-Montiel-Rold\'an for the first Dirac eigenvalue with a recent theorem of B\"ar. Moreover, we give an alternative proof of the Hijazi-Montiel-Rold\'an inequality based on the work of B\"ar and B\"ar-Ballmann.

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Simon Brendle, Raphael Tsiamis, Yipeng Wang. 2025-10-20. On fill-ins with scalar curvature bounded from below and an inequality of Hijazi-Montiel-Rold\'an. https://arxiv.org/abs/2510.17780

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