scholarly journals On weakly complete surfaces

2015 ◽  
Vol 353 (11) ◽  
pp. 969-972 ◽  
Author(s):  
Samuele Mongodi ◽  
Zbigniew Slodkowski ◽  
Giuseppe Tomassini
Keyword(s):  
Complete Surfaces

scholarly journals Some properties of Grauert type surfaces

2017 ◽  
Vol 28 (08) ◽  
pp. 1750063 ◽  
Author(s):  
Samuele Mongodi ◽  
Zbigniew Slodkowski ◽  
Giuseppe Tomassini
Keyword(s):  
Convex Space ◽  
Level Sets ◽  
Double Cover ◽  
Classification Theorem ◽  
Stein Space ◽  
Pluriharmonic Function ◽  
Exhaustion Function ◽  
Real Analytic ◽  
Complete Surfaces

In a previous work, we classified weakly complete surfaces which admit a real analytic plurisubharmonic exhaustion function; we showed that, if they are not proper over a Stein space, then they admit a pluriharmonic function, with compact Levi-flat level sets foliated with dense complex leaves. We called these Grauert type surfaces. In this note, we investigate some properties of these surfaces. Namely, we prove that the only compact curves that can be contained in them are negative in the sense of Grauert and that the level sets of the pluriharmonic function are connected, thus completing the analogy with the Cartan–Remmert reduction of a holomorphically convex space. Moreover, in our classification theorem, we had to pass to a double cover to produce the pluriharmonic function; the last part of the present paper is devoted to the construction of an example where passing to a double cover cannot be avoided.

scholarly journals Chern–Osserman type equality for complete surfaces inRn

2018 ◽  
Vol 129 ◽  
pp. 117-124
Author(s):  
Qing Chen ◽  
Wenjie Yang
Keyword(s):  
Complete Surfaces

Labeling Complete Surfaces in Scene Understanding

2014 ◽  
Vol 112 (2) ◽  
pp. 172-187 ◽  
Author(s):  
Ruiqi Guo ◽  
Derek Hoiem
Keyword(s):  
Scene Understanding ◽  
Complete Surfaces

On the Gauss map of complete surfaces of constant mean curvature in R3 and R4

1982 ◽  
Vol 57 (1) ◽  
pp. 519-531 ◽  
Author(s):  
D. A. Hoffman ◽  
R. Osserman ◽  
R. Schoen
Keyword(s):  
Mean Curvature ◽  
Constant Mean Curvature ◽  
Gauss Map ◽  
Complete Surfaces
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