Inserted: 21 oct 2022
Last Updated: 21 oct 2022
Journal: Comptes Rendus Mathematique
We consider the classical "Serrin symmetry result" for the overdetermined boundary value problem related to the equation $\Delta u=-1$ in a model manifold of non-negative Ricci curvature. Using an extension of the Weinberger classical argument we prove a Euclidean symmetry result under a suitable "compatibility" assumption between the solution and the geometry of the model.