Wei, Shihshu Walter

On 1-harmonic functions

SIGMA, Symmetry Integrability Geom. Methods Appl. 3, Paper 127, 10 p., electronic only (2007)


Summary: Characterizations of entire subsolutions for the 1-harmonic equation of a constant 1-tension field are given with applications in geometry via transformation group theory. In particular, we prove that every level hypersurface of such a subsolution is calibrated and hence is area-minimizing over R; and every 7-dimensional $SO(2) \times SO(6)$-invariant absolutely area-minimizing integral current in $R^{8}$ is real analytic. The assumption on the $SO(2) \times SO(6)$-invariance cannot be removed, due to the first counter-example in $R^{8}$, proved by Bombieri, De Girogi and Giusti.

Mathematics Subject Classification

53C40, 53C42


1-harmonic function, 1-tension field, absolutely area-minimizing integral current