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Scalar curvature rigidity of small spherical caps with arbitrary fill-ins
Yiyue Zhang, Bowen Zhao
We prove an analogue of Min-Oo's conjecture for sufficiently small spherical caps in the unit round sphere. For every dimension , there exists such that the follo…
Stability of the Riemannian positive mass theorem in all dimensions
Gaoming Wang, Yiyue Zhang
We prove stability of the Riemannian positive mass theorem in all dimensions, extending the Dong-Song stability theorem. For a sequence of complete asymptotically flat manifolds wi…
The Hyperboloidal and Spacetime Positive Mass Theorem in All Dimensions
Sven Hirsch, Marcus Khuri, Martin Lesourd +1
Using the recent work of Brendle--Wang on the Riemannian positive mass theorem, we prove the spacetime positive mass theorem for asymptotically flat and asymptotically hyperboloida…
Rigidity of Asymptotically Hyperboloidal Initial Data Sets with Vanishing Mass
Sven Hirsch, Hyun Chul Jang, Yiyue Zhang
In Special Relativity, massless objects are characterized as either vacuum states or as radiation propagating at the speed of light. This distinction extends to General Relativity…
Stability of Llarull's theorem in all dimensions
Sven Hirsch, Yiyue Zhang
Llarull's theorem characterizes the round sphere among all spin manifolds whose scalar curvature is bounded from below by . In this paper we show that if the scalar c…
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…