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math.DG2024
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…
gr-qc2024
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…
math-ph2024
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…