8 citations · 24 across the 25 of their papers we have counts for
28 papers
Compact Proof of the Positivity of Quasi-Local Masses for a class of Initial Data
Puskar Mondal, Shing-Tung Yau
We prove a purely quasi-local positivity theorem for the Wang--Yau mass for a class of initial data whose Jang deformation, after a boundary-preserving conformal reduction to zero…
Boundary-Geometry-Driven Black Hole Formation in Vacuum
Dipanjan Dey, Puskar Mondal, Shing-Tung Yau
We identify a boundary-geometry-driven mechanism for the dynamical formation of marginally outer trapped surfaces (MOTSs) in vacuum general relativity. Mild three-dimensional aniso…
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
We prove a sharp volume-stability theorem for closed hyperbolic three-manifolds. Let \((M,h)\) be closed hyperbolic with \(\operatorname{Ric}_h=-2h\), and let \(g_i\) be smooth met…
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…
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…
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 \(Λ\) on globally hy…
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 sphe…
A new conformal quasi-local energy in general relativity
Puskar Mondal, Shing-Tung Yau
We construct new conserved quasi-local energies in general relativity using the formalism developed by \cite{CWY}. In particular, we use the optimal isometric embedding defined in…
Quasi-local masses in General relativity and their positivity: Spinor approach
Puskar Mondal, Shing-Tung-Yau
We study the quasi-local masses arising in general relativity using spinors and prove their positivity property. This leads to the question of a pure quasi-local proof of the posit…
Mass and infinite dimensional geometry
Puskar Mondal
I unravel an elegant geometric meaning of the mass of the lowest energy excited state of a renormalizable quantized field theory by studying the weighted geometry of the classical…
Formation of trapped surfaces in the Einstein-Yang-Mills system
Nikolaos Athanasiou, Puskar Mondal, Shing-Tung Yau
We prove a scale-invariant, semi-global existence result and a trapped surface formation result in the context of coupled Einstein-Yang-Mills theory, without symmetry assumptions.…
A Geometric Approach to the Yang-Mills Mass Gap
Puskar Mondal
I provide a new idea based on geometric analysis to obtain a positive mass gap in pure non-abelian renormalizable Yang-Mills theory. The orbit space, that is the space of connectio…
On the Global Well-Posedness of the Einstein-Yang-Mills System
Petar Griggs, Puskar Mondal
In this paper, we present a partial result on the global well-posedness of the Cauchy problem for the Einstein-Yang-Mills system in the constant mean extrinsic curvature spatial ha…
Global exterior stability of the Minkowski space: coupled Einstein-Yang-Mills perturbations
Puskar Mondal, Shing-Tung Yau
Here we prove a global gauge-invariant radiation estimates for the perturbations of the dimensional Minkowski spacetime in the presence of Yang-Mills sources. In particular,…
Continuation Criterion For Solutions To The Einstein Equations
Oswaldo Vazquez, Puskar Mondal
We prove a continuation condition in the context of 3+1 dimensional vacuum Einstein gravity in Constant Mean extrinsic Curvature (CMC) gauge. More precisely, we obtain quantitative…
Einstein-Yang-Mills equations in the double null framework
Puskar Mondal, Shing-Tung Yau
We prove a semi-global gauge-invariant estimate for the solutions of the characteristic initial value problem associated with the coupled Einstein-Yang-Mills equations. In particul…
The nonlinear stability of n+1 dimensional FLRW spacetimes
Puskar Mondal
We prove nonlinear Lyapunov stability of a family of `'-dimensional cosmological models of general relativity locally isometric to the Friedman Lemaître Robertson Walker (FLRW…
Aspects of Quasi-local energy for gravity coupled to gauge fields
Puskar Mondal, Shing-Tung Yau
We study the aspects of quasi-local energy associated with a surface bounding a space-like domain of a physical dimensional spacetime in the regime of gravity cou…
Local well-posedness of the Einstein-Yang-Mills system in CMCSHGC gauge
Puskar Mondal
We study the local well-posedness of the Einstein-Yang-Mills equations in constant mean extrinsic curvature spatial harmonic generalized Coulomb gauge (CMCSHGC). In this choice of…
Einstein flow with matter sources: stability and convergence
Vincent Moncrief, Puskar Mondal
Two recent articles \cite{ashtekar2015general, moncrief2019could} suggested an interesting dynamical mechanism within the framework of the vacuum Einstein flow (or Einstein- flo…
On the non-blow up of energy critical nonlinear massless scalar fields in `3+1' dimensional globally hyperbolic spacetimes: Light cone estimates
Puskar Mondal
Here we prove a global existence theorem for the solutions of the semi-linear wave equation with critical non-linearity admitting a positive definite Hamiltonian. Formulating a par…
The linear stability of the Einstein-Euler system on negative Einstein spaces
Puskar Mondal
Here we prove the linear stability of a family of `'-dimensional Friedmann Lemaître Robertson Walker (FLRW) cosmological models of general relativity. We show that the solutio…
Big-bang limit of gravity and Thurston boundary of Teichmüller space
Puskar Mondal
We study the asymptotic behavior of the solution curves of the dynamics of spacetimes of the topological type , , where is a closed Riemann sur…