RAMIFICATION OVER HYPERSURFACES LOCATED IN SUBGENERAL POSITION OF THE GAUSS MAP OF COMPLETE MINIMAL SURFACES WITH FINITE TOTAL CURVATURE

Abstract

The first aim of this paper is to show the second main theorem for holomorphic maps from a compact Riemann surface into the complex projective space which is ramified over hypersurfaces in subgeneral position. We then use it to study the ramification over hypersurfaces of the generalized Gauss map of complete regular minimal surfaces in Rm with finite total curvature, sharing hypersurfaces in subgeneral position. The results generalize our previous results [Thai and Thoan, Vietnam J. Math. 2017, doi:10.1007/s10013-017-0259-6].