On the characterization of minimal surfaces with finite total curvature in $${\mathbb {H}}^2\times {\mathbb {R}}$$ H 2 × R and $$\widetilde{\mathrm{PSL}}_2 ({\mathbb {R}})$$ PSL ~ 2 ( R )

2019 ◽  
Vol 58 (2) ◽  
Author(s):  
Laurent Hauswirth ◽  
Ana Menezes ◽  
Magdalena Rodríguez
Keyword(s):  
Minimal Surfaces ◽  
Total Curvature ◽  
Finite Total Curvature

scholarly journals On the Gauss map of minimal surfaces with finite total curvature

1991 ◽  
Vol 44 (2) ◽  
pp. 225-232 ◽  
Author(s):  
Min Ru
Keyword(s):  
Minimal Surface ◽  
Minimal Surfaces ◽  
General Position ◽  
Total Curvature ◽  
Gauss Map ◽  
Finite Total Curvature

We prove that if a nonflat complete regular minimal surface immersed in Rn is of finite total curvature, then its Gauss map can omit at most (n – 1)(n + 2)/2 hyperplanes in general position in Pn–1 (ℂ).

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