On the stability of free boundary minimal submanifolds in conformal domains

Abstract

Given an $n$-dimensional Riemannian manifold with non-negative sectional curvature and convex boundary, that is conformal to a Euclidean convex bounded domain, we show that it does not contain any compact stable free boundary minimal submanifold of dimension $2\le k\le n-2$, provided that either the boundary is strictly convex with respect to any of the two metrics or the sectional curvature is strictly positive.