scholarly journals The Gaussian Image of Mean Curvature One Surfaces in $\mathbb{H}^3$ of Finite Total Curvature

2018 ◽  
Author(s):  
Pascal Collin ◽  
Laurent Hauswirth ◽  
Harold Rosenberg
Keyword(s):  
Mean Curvature ◽  
Total Curvature ◽  
Gaussian Image ◽  
Finite Total Curvature

The focusing of radiation by a random surface when the source is at a finite distance

1960 ◽  
Vol 56 (1) ◽  
pp. 27-40 ◽  
Author(s):  
M. S. Longuet-Higgins
Keyword(s):  
Mean Curvature ◽  
Joint Distribution ◽  
Total Curvature ◽  
Statistical Distribution ◽  
Constant Parameter ◽  
Random Surface ◽  
Second Derivatives ◽  
Finite Distance ◽  
The Mean ◽  
Image Position

Imagine a nearly horizontal, statistically uniform, random surface ζ(x, y), Gaussian in the sense that the second derivatives , , have a normal joint distribution. The problem considered is the statistical distribution of the quantitywhere J and Ω denote the mean curvature and total curvature of the surface, respectively, and ν is a constant parameter.

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