About the Lorentzian Yamabe problem

Nicolas Ginoux (1, 2)

1 UR - Universität Regensburg
2 IECL - Institut Élie Cartan de Lorraine

We investigate the solutions to the Yamabe problem on globally hyperbolic spacetimes. On standard static spacetimes, we prove the existence of global solutions and show with the help of examples that uniqueness does not hold in general.

Mots clés: nonlinear hyperbolic equations; Lorentzian geometry; Yamabe problem; globally hyperbolic spacetimes; Cauchy problem

Domaines: Géométrie différentielle [math.DG]; Equations aux dérivées partielles [math.AP]

Nicolas Ginoux. About the Lorentzian Yamabe problem. Geometriae Dedicata, 2015, 174 (1), pp.287-309. ⟨10.1007/s10711-014-0018-8⟩. ⟨hal-01265984⟩