From the 1 of 6 linked papers with an AI index.
6 papers
Formation of trapped surfaces for the spherically symmetric Einstein-Yang-Mills system with non-trivial incoming data
Nikolaos Athanasiou, Puskar Mondal, Shing-Tung Yau
We establish a trapped surface formation theorem for the spherically symmetric Einstein Yang Mills equations in a double-null gauge. The theorem concerns characteristic initial dat…
Volume Stability for Hyperbolic Manifolds and Applications to General Relativity
Puskar Mondal, Shing-Tung Yau
The paper proves that for closed hyperbolic 3‑manifolds, any sequence of metrics with scalar curvature ≥ −6 whose volumes approach the hyperbolic volume must converge in the C⁰ sen…
Semi-Global Existence and Trapped Surface Formation for the Einstein-Vlasov System
Nikolaos Athanasiou, Puskar Mondal, Shing-Tung Yau
In this article, we study the Einstein-Vlasov system for massless particles. Our main contribution is the provision of a novel method for controlling the Vlasov matter in a double…
Dynamical Formation of Black Holes due to Boundary Effect in Vacuum Gravity
Puskar Mondal, Shing-Tung Yau
We prove the dynamical formation of a marginally outer trapped surface in pure vacuum spacetime from smooth asymptotically flat Cauchy data which initially contain no MOTS. The mec…
A large data result for vacuum Einstein's equations
Puskar Mondal
We prove a global well-posedness and asymptotic convergence theorem for the \((3+1)\)-dimensional vacuum Einstein equations with positive cosmological constant \(Î\) on globally h…
On a Rigidity Result in Positive Scalar Curvature Geometry
Puskar Mondal
I prove a scalar curvature rigidity theorem for spheres. In particular, I prove that geodesic balls of radii strictly less than in dimensional unit sph…