Exponentially harmonic maps, exponential stress energy and stability (Q2828651)

Exponentially harmonic maps are critical points of the exponential energy \(E_e(f):=\int\exp(|df|^2/2)\,dx\). The paper studies basic aspects of exponentially harmonic maps of which there are well-known counterparts for harmonic maps. A suitable stress-energy tensor is defined, and applied to the description of horizontally weakly conformal exponentially harmonic maps. As a second topic, basic stability criteria are derived for exponentially harmonic maps. Finally, there is also a study of the interplay between properties of an isometric immersion and its Gauss map in terms of exponential harmonicity.