On the existence and conformal equivalence of extremal maps of various types (Q1346799)

Motivated by the work of \textit{J. Eells} and \textit{M. J. Ferreira} [Bull. Lond. Math. Soc. 23, No. 2, 160-162 (1991; Zbl 0704.58014)], the author studies the existence problem of extremal maps \(\varphi: M\to N\) between Riemannian manifolds, where extremality is with respect to the functionals \(E(f)= \int_M |df|^2 v_g\), \(E_e (f)= \int_M e^{|df|^2 /2}v_g\), \(E_p (f)= \int_M |df|^p v_g\) and \(E^1_p (f)= \int_M (1+ |df |^2 )^{p/2} v_g\). Allowing conformal change of the metric on the domain, various existence results are derived. It is also shown that some of the extremal maps are equivalent under this type of conformal change.