3 papers
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…
gr-qc2025
Monotonicity of Causal Killing Vectors and Geometry of ADM Mass Minimizers
Sven Hirsch, Lan-Hsuan Huang
We address two problems concerning the ADM mass-minimizing initial data sets. First, we show that the equality case of the positive mass theorem embeds into a pp-wave spacetime. Se…