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arXiv · 2608.06935

Rigidity for spin fill-ins with scalar curvature bounded from below

Bernd Ammann·Samuel Lockman
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Abstract

We establish the rigidity statement in the equality case of the hyperspherical-radius inequality of Brendle, Tsiamis, and Wang for compact spin fill-ins with scalar curvature bounded below. More precisely, let $(M^{n\geq 3},g)$ be a compact, connected Riemannian spin manifold having a connected boundary $\Sigma$ and scalar curvature satisfying $\mathrm{scal}_g\geq -n(n-1)$. We prove that equality in the upper bound \[ \inf_{\Sigma}H\leq (n-1)\sqrt{1+\operatorname{Rad}(\Sigma)^{-2}} \] given by Brendle, Tsiamis, and Wang holds if and only if $(M,g)$ is isometric to a geodesic ball in hyperbolic space.

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Bernd Ammann, Samuel Lockman. 2026-08-07. Rigidity for spin fill-ins with scalar curvature bounded from below. https://arxiv.org/abs/2608.06935

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