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arXiv · 2607.09472

Scalar Curvature Rigidity for Products of convex Hypersurfaces and even dimensional Manifolds

Georg Frenck·Thomas Schick·Lukas Schönlinner
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Abstract

We give a proof of scalar curvature rigidity in the spirit of Llarull and Goette-Semmelmann for products of strictly convex hypersurfaces in Euclidean space and nonnegatively curved spaces with non-vanishing Euler-characteristic. Our proof is based on the Fredholm family index theorem. This recovers corresponding results of Lockman-Zeidler where Clifford-linear (family) index theory is used.

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Georg Frenck, Thomas Schick, Lukas Schönlinner. 2026-07-10. Scalar Curvature Rigidity for Products of convex Hypersurfaces and even dimensional Manifolds. https://arxiv.org/abs/2607.09472

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