The Value Distribution of Gauss Maps of Immersed Harmonic Surfaces with Ramification

Motivated by the result of Chen-Liu-Ru [1], we investigate the value distribution properties for the generalized Gauss maps of weakly complete harmonic surfaces immersed in ℝn with ramification, which can be seen as a generalization of the results in the case of the minimal surfaces. In addition, we give an estimate of the Gauss curvature for the K-quasiconfomal harmonic surfaces whose generalized Gauss map is ramified over a set of hyperplanes.