Stability of \(F\)-harmonic maps into pinched manifolds (Q5935597)

For a smooth map \(\varphi:(M,g) \to(N,h)\) between Riemannian manifolds and a \(C^2\) strictly increasing function \(F:[0,\infty) \to[0,\infty)\), the \(F\)-energy \(E_F(\varphi)\) is defined by NEWLINE\[NEWLINEE_F(\varphi)= \int_MF\left( {|_d \varphi |^2 \over 2}\right) v_g,NEWLINE\]NEWLINE where \(v_g\) is the volume element of \((M,g)\). A critical point \(\varphi\) of \(E_F(\varphi)\) is called an \(F\)-harmonic map.NEWLINENEWLINENEWLINETwo stability theorems due to \textit{R. Howard} [Mich. Math. J. 32, 321-334 (1985; Zbl 0591.49030)] and \textit{T. Okayasu} [Tôhoku Math. J., II. Ser. 40, No. 2, 213-220 (1988; Zbl 0652.58021)] are extended here to the case of \(F\)-harmonic maps, by showing that every stable \(F\)-harmonic map into a sufficiently pinched simply connected Riemannian manifold is constant.