Some results on harmonic maps (Q2875932)

This is mostly an overview over some by-now classical results on harmonic maps and their heat flow, notably the Eells/Sampson existence proof using the heat flow method, the Schoen/Uhlenbeck partial regularity result, and the existence of harmonic spheres in certain homotopy classes proved by \textit{J. Sacks} and \textit{K. Uhlenbeck} [Ann. Math. (2) 113, 1--24 (1981; Zbl 0462.58014)]. For the latter result, there is a new proof here which uses the Moser-Trudinger inequality.