Eine Bemerkung zur Regularität stationärer Punkte von konform invarianten Variationsintegralen. (A remark on the regularity of stationary points of conformally invariant variational integrals) (Q1076964)

An elementary argument is given which reduces the regularity problem for two-dimensional stationary harmonic maps to the corresponding result for stationary minimal surfaces. This question had already been solved by the author in the affirmative [see Manuscr. Math. 47, 85-104 (1984; Zbl 0543.49020); J. Reine Angew. Math. 329, 1-15 (1981; Zbl 0461.53029)]. The result is actually shown to be true for the more general class of conformally invariant variational integrals. A different proof by \textit{R. M. Schoen} [Publ., Math. Sci. Res. Inst. 2, 321-358 (1984; Zbl 0551.58011)] which established the same reduction uses a removability theorem for isolated singularities of harmonic maps by \textit{J. Sacks} and \textit{K. Uhlenbeck} [Ann. Math., II. Ser. 113, 1-24 (1981; Zbl 0462.58014)]. Still very little is known about the regularity of weak solutions to the harmonic map equations.