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math.DG2026
The lock principle for scalar curvature
Georg Frenck, Bernhard Hanke, Sven Hirsch
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…
math.DG2026
Surgery and total mean curvature
Georg Frenck, Bernhard Hanke, Sven Hirsch
We prove Gromov's conjecture on the total mean curvature of fill-ins in various cases. Our methods are based on surgery to reduce the statement to fill-ins of spheres, which can be…
math.DG2026
A universal Bochner formula for scalar curvature
Sven Hirsch
We introduce a universal Bochner formula for scalar curvature that contains, as special cases, the stability inequality for minimal slicings, a Schrödinger-Lichnerowicz-type formul…