Acta mathematica scientia,Series B ›› 2022, Vol. 42 ›› Issue (1): 172-186.doi: 10.1007/s10473-022-0109-9

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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).

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

CLC Number: 

  • 32H25
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