In this article, we study the ramification of the holomorphic map ramificate over hyperplanes in nsubgeneral position in ( ) k . This work is a continuation of previous work of Dethloff-Ha [1]. We thus give an improvement of the results by studying the holomorphic maps with ramification of M. Ru [3] and Dethloff-Ha. | Nguyễn Thị Ngọc Ánh Tạp chí KHOA HỌC & CÔNG NGHỆ 128(14): 127 - 131 AN ESTIMATE FOR HOLOMORPHIC MAP RAMIFICATED OVER HYPERPLANES IN SUBGENERAL POSITION Pham Duc Thoan1, Pham Hoang Ha2, Tran Hue Minh3 2Hanoi 1National University of Civil Engineering, National University of Education, 3College of Education - TNU SUMMARY In this article, we study the ramification of the holomorphic map ramificate over hyperplanes in nk subgeneral position in ( ) . This work is a continuation of previous work of Dethloff-Ha [1]. We thus give an improvement of the results by studying the holomorphic maps with ramification of M. Ru [3] and Dethloff-Ha [1]. Key words: Minimal surface, Gauss map, Ramification, holomorphic map, Value distribution theory. INTRODUCTION* In 1993, M. Ru [3] studied the holomorphic maps in k ( ) with ramification. The aim of this work is that studying the distribution of Gauss map of Minimal surface. Using the notations which will be introduced in §2, the result of Ru can be stated as following. Main Lemma [3] Let k f ( f 0 :.: f k ) : R ( ) be a nondegenerate holomorphic map, H 0 ,., H q be hyperplanes in k ( ) in n subgeneral position, and ( j ) be their Nochka weights. , f k ) : R k 1 {0} is reduced representation of f . Assume that q 2n k 1 and Let F ( f0 , q 2q / N ( j) (k 1) q q ( j ) (k 1) (k Recently, the authors . Ha and D. Dethloff [1] gave a version on the lower dimension spaces ( 1 ( ) . Theorem (Lemma 8, [1]) For every with q 1 q 0 and j 1 m j q 2 |F ( H j ) |4/ N | Fk |1 2 q / N |F ( H j ) | ( j ) j 1 p 0 q j 1 k 1 2R C 2 2 R | z| k ( k 1) ( k p )2 q / N 2 p 0 , q q 2 Tel: 0985 130218, Email: 134 m j q j 1 || f || 1 | W ( f 0 , f1 ) | C0 2R . R | z |2 2 In this paper we will consider the corresponding problem for the holomorphic R {z :|z| 1. Then there exists some positive constant
