Value distribution properties for Gauss maps of immersed harmonic surfaces ramified over hypersurfaces

In this paper, we study the value distribution properties of the generalized Gauss maps of weakly complete harmonic surfaces immersed in ℝ^m, which is the case where the generalized Gauss map Φ is ramified over a family of hypersurfaces {Q_j} _j=1 ^q in ℙ^m−1 (ℂ) located in the N-subgeneral position. In addition, we investigate the Gauss curvature estimate for the K-quasiconformal harmonic surfaces immersed in ℝ³ whose Gauss maps are ramified over a family of hypersurfaces located in the N-subgeneral position.