Calculus of Variations and Geometric Measure Theory

A. Roncoroni

A Serrin-type symmetry result on model manifolds: an extension of the Weinberger argument

created by roncoroni on 05 Nov 2020


Accepted Paper

Inserted: 5 nov 2020
Last Updated: 5 nov 2020

Journal: Comptes Rendus Mathematique
Year: 2018

ArXiv: 1708.02032 PDF


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.