Complete surfaces in H 3 with a constant principal curvature

Author(s):  
Zhisheng Ma
Author(s):  
Hongli Deng ◽  
Wei Zhang ◽  
Eric Mortensen ◽  
Thomas Dietterich ◽  
Linda Shapiro

1951 ◽  
Vol 18 (3) ◽  
pp. 251-252
Author(s):  
Murray Kornhauser

Abstract Surface deformation of elastic bodies having the same modulus is treated by the standard texts on elasticity, but the applicability of the solution is limited to the range of the tables of coefficients presented. This note extends the tables to cover the range that applies to bodies having one principal curvature much larger than the other. Some inaccuracy in the tables in current use also is noted. The reader is referred to any good text on elasticity for a general discussion of this problem.


2017 ◽  
Vol 28 (08) ◽  
pp. 1750063 ◽  
Author(s):  
Samuele Mongodi ◽  
Zbigniew Slodkowski ◽  
Giuseppe Tomassini

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.


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

Author(s):  
D. N. H. Thanh ◽  
D. Sergey ◽  
V. B. Surya Prasath ◽  
N. H. Hai

<p><strong>Abstract.</strong> Diabetes is a common disease in the modern life. According to WHO’s data, in 2018, there were 8.3% of adult population had diabetes. Many countries over the world have spent a lot of finance, force to treat this disease. One of the most dangerous complications that diabetes can cause is the blood vessel lesion. It can happen on organs, limbs, eyes, etc. In this paper, we propose an adaptive principal curvature and three blood vessels segmentation methods for retinal fundus images based on the adaptive principal curvature and images derivatives: the central difference, the Sobel operator and the Prewitt operator. These methods are useful to assess the lesion level of blood vessels of eyes to let doctors specify the suitable treatment regimen. It also can be extended to apply for the blood vessels segmentation of other organs, other parts of a human body. In experiments, we handle proposed methods and compare their segmentation results based on a dataset – DRIVE. Segmentation quality assessments are computed on the Sorensen-Dice similarity, the Jaccard similarity and the contour matching score with the given ground truth that were segmented manually by a human.</p>


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