New Solutions to the Serrin Problem on Riemannian Manifolds

Abstract: The Serrin problem is an overdetermined elliptic problem that shares many analogies with the theory of constant mean curvature surfaces.

In these two talks, we will revisit some known results related to the existence and classification of solutions to the Serrin problem on certain Riemannian manifolds.

Motivated by these works, we will use bifurcation theory to demonstrate the existence of non-trivial domains that admit solutions to the Serrin problem on cohomogeneity one Riemannian manifolds.

This is joint work with Renato Bettiol (CUNY).