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8 papers · 2 filters
A Hopf theorem for non-constant mean curvature and a conjecture of A.D. Alexandrov
Jose A. Galvez, Pablo Mira
We prove a uniqueness theorem for immersed spheres of prescribed (non-constant) mean curvature in homogeneous three-manifolds. In particular, this uniqueness theorem proves a conje…
A connection between flat fronts in hyperbolic space and minimal surfaces in euclidean space
Antonio Martínez, Pedro Roitman, Keti Tenenblat
A geometric construction is provided that associates to a given flat front in a pair of minimal surfaces in which are related by a Ribaucour transform…
A holographic principle for the existence of parallel spinor fields and an inequality of Shi-Tam type
Oussama Hijazi, Sebastián Montiel
Suppose that is the -dimensional boundary of a connected compact Riemannian spin manifold with non-negative scalar curvature, and that…
A holographic principle for the existence of imaginary Killing spinors
Oussama Hijazi, Simon Raulot, Sebastian Montiel
Suppose that is the -dimensional boundary, with positive (inward) mean curvature , of a connected compact -dimensional Riemannian spin manifold $(Ω^{n+1}…
Uniqueness of the de Sitter spacetime among static vacua with positive cosmological constant
Oussama Hijazi, Simon Raulot, Sebastian Montiel
We prove that, among all (n + 1)-dimensional spin static vacua with positive cosmological constant, the de Sitter spacetime is characterized by the fact that its spatial Killing ho…
On a Liu--Yau type inequality for surfaces
Oussama Hijazi, Simon Raulot, Sebastian Montiel
Let be a compact and mean-convex domain with smooth boundary , in an initial data set , which has no apparent horizon in its interior. If is spacel…