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arXiv · 2602.10932

The lock principle for scalar curvature

Georg Frenck·Bernhard Hanke·Sven Hirsch
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Abstract

We prove a Riemannian positive mass theorem for asymptotically flat spin manifolds with hypersurface singularities. Unlike earlier results, some components of the singular set may be mean-concave, provided that other components of the singular set are sufficiently mean-convex. Our proof uses initial data sets where a suitably chosen second fundamental form transfers convexity defects between different singularity components.

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Georg Frenck, Bernhard Hanke, Sven Hirsch. 2026-02-11. The lock principle for scalar curvature. https://arxiv.org/abs/2602.10932

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