Stability of F-stationary maps of a class of functionals related to conformal maps

Abstract

In this paper, we study a generalized functional Φ_F related to the conformality of maps between Riemannian manifolds. We derive the first variation formula and the second variation formula of Φ_F, then we study the stability of F-stationary map from or into the standard sphere. We also introduce the F-stress energy tensor associated to Φ_F which is naturally linked to conservation law.