数学物理学报(英文版) ›› 2022, Vol. 42 ›› Issue (1): 172-186.doi: 10.1007/s10473-022-0109-9

• 论文 • 上一篇    下一篇

THE VALUE DISTRIBUTION OF GAUSS MAPS OF IMMERSED HARMONIC SURFACES WITH RAMIFICATION

刘志学1, 李叶舟1, 陈行堤2   

  1. 1. School of Science, Beijing University of Posts and Telecommunications, Beijing, 100876, China;
    2. School of Mathematical Sciences, Huaqiao University, Quanzhou, 362021, China
  • 收稿日期:2020-07-25 修回日期:2021-06-11 出版日期:2022-02-25 发布日期:2022-02-24
  • 通讯作者: Zhixue LIU,E-mail:zxliumath@bupt.edu.cn E-mail:zxliumath@bupt.edu.cn
  • 作者简介:Yezhou LI,E-mail:yezhouli@bupt.edu.cn;Xingdi CHEN,E-mail:chxtt@hqu.edu.cn
  • 基金资助:
    The first author was supported by the Fundamental Research Funds for the Central Universities (500421360). The second author was supported by NNSF of China (11571049, 12071047). The third named author was supported by NNSF of China (11971182), NSF of Fujian Province of China (2019J01066).

THE VALUE DISTRIBUTION OF GAUSS MAPS OF IMMERSED HARMONIC SURFACES WITH RAMIFICATION

Zhixue LIU1, Yezhou LI1, Xingdi CHEN2   

  1. 1. School of Science, Beijing University of Posts and Telecommunications, Beijing, 100876, China;
    2. School of Mathematical Sciences, Huaqiao University, Quanzhou, 362021, China
  • Received:2020-07-25 Revised:2021-06-11 Online:2022-02-25 Published:2022-02-24
  • Contact: Zhixue LIU,E-mail:zxliumath@bupt.edu.cn E-mail:zxliumath@bupt.edu.cn
  • Supported by:
    The first author was supported by the Fundamental Research Funds for the Central Universities (500421360). The second author was supported by NNSF of China (11571049, 12071047). The third named author was supported by NNSF of China (11971182), NSF of Fujian Province of China (2019J01066).

摘要: 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 $\Bbb{R}^n$ 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.

关键词: value distribution, harmonic surfaces, quasiconformal mappings, conformal metric, Gauss map

Abstract: 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 $\Bbb{R}^n$ 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.

Key words: value distribution, harmonic surfaces, quasiconformal mappings, conformal metric, Gauss map

中图分类号: 

  • 32H25