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math.DG2026
Curvature inequalities and rigidity for constant mean curvature and spacetime constant mean curvature surfaces
Alejandro Peñuela Diaz
We establish curvature inequalities and rigidity results for surfaces satisfying constant mean curvature type conditions in both Riemannian and Lorentzian geometry. In the Riemanni…
math.DG2025
Foliations by critical surfaces of the Hawking energy in asymptotically flat initial data sets
Alejandro Peñuela Diaz
Area-constrained critical surfaces for the Hawking quasi-local energy ("Hawking surfaces") provide a natural setting for that energy: they enjoy positivity and rigidity properties.…
math.DG2021★ 2 cited
Constructing electrically charged Riemannian manifolds with minimal boundary, prescribed asymptotics, and controlled mass
Armando J. Cabrera Pacheco, Carla Cederbaum, Penelope Gehring +1
In 2015, Mantoulidis and Schoen constructed -dimensional asymptotically Euclidean manifolds with non-negative scalar curvature whose ADM mass can be made arbitrarily close to th…