A vanishing result for the supersymmetric nonlinear sigma model in higher dimensions

Abstract

We prove a vanishing result for critical points of the supersymmetric nonlinear sigma model on complete Riemannian manifolds of positive Ricci curvature in higher dimensions, that is for domains of dimension \(n\) bigger than two, under energy assumptions. More precisely, we demand that the \(L^p\)-norm of the energy associated to the supersymmetric nonlinear sigma model is finite and its \(L^n\)-norm sufficiently small, where \(2<p<n\).