6 papers
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…
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…
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…
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…
Rigidity of spin fill-ins with non-negative scalar curvature
Simone Cecchini, Sven Hirsch, Rudolf Zeidler
We establish new mean curvature rigidity theorems for spin fill-ins with non-negative scalar curvature using two different spinorial techniques. Our results address two questions b…
Uniqueness of blowups for forced mean curvature flow
Sven Hirsch, Jonathan J. Zhu
We prove uniqueness of tangent cones for forced mean curvature flow, at both closed self-shrinkers and round cylindrical self-shrinkers, in any codimension. The corresponding resul…