10 citations · 32 across the 22 of their papers we have counts for
5 papers · 1 filter
Monotone quantities of -harmonic functions and their applications
Sven Hirsch, Pengzi Miao, Luen-Fai Tam
We derive local and global monotonic quantities associated to -harmonic functions on manifolds with nonnegative scalar curvature. As applications, we obtain inequalities relatin…
Hawking Mass Monotonicity for Initial Data Sets
Sven Hirsch
We introduce new systems of PDE on initial data sets whose solutions model double-null foliations. This allows us to generalize Geroch's monotonicity formula for the Hawk…
Rigid comparison geometry for Riemannian bands and open incomplete manifolds
Sven Hirsch, Demetre Kazaras, Marcus Khuri +1
Comparison theorems are foundational to our understanding of the geometric features implied by various curvature constraints. This paper considers manifolds with a positive lower b…
A generalization of Geroch's conjecture
Simon Brendle, Sven Hirsch, Florian Johne
The Theorem of Bonnet--Myers implies that manifolds with topology do not admit a metric of positive Ricci curvature, while the resolution of Geroch's…
The case of equality for the spacetime positive mass theorem
Sven Hirsch, Yiyue Zhang
The rigidity of the spacetime positive mass theorem states that an initial data set satisfying the dominant energy condition with vanishing mass can be isometrically embe…