Some analytic results on interpolating sesqui-harmonic maps (Q2196673)

The so-called interpolating sesqui-harmonic maps studied in this paper are maps between Riemannian manifolds which are critical points of the functional \[ E_{c_1, c_2}(\phi)=c_1\int_M |d\phi|^2dv_g+c_2\int_M |\tau(\phi)|^2dv_g, \] where \(c_1\) and \(c_2\) are constants. The equation of such maps can be written as \[ c_1\tau(\phi)+c_2\tau_2(\phi)=0,\tag{a} \] where \(\tau(\phi)\) and \(\tau_2(\phi)\) are the tension and the bitension fields of the map \(\phi\) respectively. Note that such maps are equivalent to those ``\(\lambda\)-biharmonic maps'' defined in [\textit{B.-Y. Chen}, Total mean curvature and submanifolds of finite type. 2nd ed. Hackensack, NJ: World Scientific (2015; Zbl 1326.53004)]. The paper under review obtained some results on the regularity of weak interpolating sesqui-harmonic maps into spheres and a classification of interpolating sesqui-harmonic maps from Euclidean domain under some assumptions on the energy, dimensions and the signs of the constants \(c_1\) and \(c_2\) in Equation (a).