| Résume | The concept of mass for time-symmetric initial data has been extensively explored
and is now a cornerstone in the study of contemporary Mathematical General
Relativity, especially in relation to spacetimes with zero or negative cosmological
constants. However, the case of a positive cosmological constant presents a distinct
challenge: the renowned counterexamples to the Min-Oo conjecture by Brendle,
Marques, and Neves highlight that even the rigidity statement in a potential positive
mass theorem has not been correctly identified yet in this context.
In this presentation, I will propose a novel approach to overcome this issue, leading to
insights on a new notion of mass and to a characterization of the de-Sitter spacetime.
This is a joint work with Virginia Agostiniani and Lorenzo Mazzieri.
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