CMS/SMC
Canadian Mathematical Society
www.cms.math.ca
Canadian Mathematical Society
  location:  PublicationsjournalsCMB
Publications        
Abstract view

A note on a unicity theorem for the Gauss maps of complete minimal surfaces in Euclidean four-space

  • Pham Hoang Ha,
    Department of Mathematics, Hanoi National University of Education, 136, XuanThuy str., Hanoi, Vietnam
  • Yu Kawakami,
    Faculty of Mathematics and Physics, Institute of Science and Engineering, Kanazawa University, Kanazawa, 920-1192, Japan
Format:   LaTeX   MathJax   PDF  

Abstract

The classical result of Nevanlinna states that two nonconstant meromorphic functions on the complex plane having the same images for five distinct values must be identically equal to each other. In this paper, we give a similar uniqueness theorem for the Gauss maps of complete minimal surfaces in Euclidean four-space.
Keywords: minimal surface, Gauss map, unicity theorem minimal surface, Gauss map, unicity theorem
MSC Classifications: 53A10, 30D35, 53C42 show english descriptions Minimal surfaces, surfaces with prescribed mean curvature [See also 49Q05, 49Q10, 53C42]
Distribution of values, Nevanlinna theory
Immersions (minimal, prescribed curvature, tight, etc.) [See also 49Q05, 49Q10, 53A10, 57R40, 57R42]
53A10 - Minimal surfaces, surfaces with prescribed mean curvature [See also 49Q05, 49Q10, 53C42]
30D35 - Distribution of values, Nevanlinna theory
53C42 - Immersions (minimal, prescribed curvature, tight, etc.) [See also 49Q05, 49Q10, 53A10, 57R40, 57R42]
 

© Canadian Mathematical Society, 2017 : https://cms.math.ca/