ScholarWorks@숙명여자대학교

초록

It is known that a harmonic minimal graph in 3-dimensional Euclidean space is locally either a plane or a helicoid. We prove that any harmonic minimal graph in Rn+1 is locally foliated by (n − 1)-dimensional minimal graphs. Moreover, it is proved that a harmonic minimal graph in M2 × R is locally either a horizontal level surface or a helicoid, where M2 denotes either 2-dimensional hyperbolic space H2 or the 2-dimensional unit sphere S2.

키워드