Constant Mean Curvature Surfaces with Two Ends in Hyperbolic Space
Constant Mean Curvature Surfaces with Two Ends in Hyperbolic Space
复制标题
双曲空间中具有两端的常平均曲率曲面
DOI：
10.1080/10586458.1998.10504360
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发表时间：
1998
期刊：
影响因子：
--
通讯作者：
Katsunori Sato
中科院分区：
文献类型：
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作者：
W. Rossman;Katsunori Sato
研究了欧氏空间中极小曲面与双曲空间中常平均曲率为1的曲面之间的密切关系。就像欧氏空间中的极小曲面一样，双曲空间中唯一两端为常平均曲率1的完全连通嵌入曲面是众所周知的旋转曲面：悬链曲面。与此相反，我们表明，不同于最小的surfacesin欧几里德三空间的情况下，确实存在完整的连接浸入表面的常数平均曲率1的两端在双曲空间，不是表面的革命：属一catenoid表兄弟。这些表面是感兴趣的，因为它们表明，虽然最小的表面在欧几里德三空间和surfacesof常数平均曲率1在双曲三空间是密切相关的，有本质的区别，这两组表面。我们给的证据存在的属一catenoid表兄弟是一个histoga.
We invest igate the close relationship between minimal surfaces in Euclidean three-space and surfaces of constant mean curvature 1 in hyperbolic three-space. Just as in the case of minimal surfaces in Euclidean three-space, the only complete connected embedded surfaces of constant mean curvature 1 with two ends in hyperbolic space are well-understood surfaces of revolution: the catenoid cousins. In contrast to this, we show that, unlike the case of minimal surfacesin Euclidean three-space, there do exist complete connected immersed surfaces of constant mean curvature 1 with two ends in hyperbolic space that are not surfaces of revolution: the genus-one catenoid cousins. These surfaces are of interest because they show that, although minimal surfaces in Euclidean three-spaceand surfacesof constant mean curvature 1 in hyperbolic three-space are intimately related, there are essential differences between these two sets of surfaces. The proof we give of existence of the genus-one catenoid cousins is a mathema...
影响因子：
4.9
作者：
M. Umehara;Kotaro Yamada
通讯作者：
M. Umehara;Kotaro Yamada
双曲 3 空间中总曲率较低的平均曲率 1 曲面
DOI：
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发表时间：
2000
期刊：
Advanced Studies in Pure Mathematics, Minimal surfaces, Geometric Analysis and Symplictic Geometry 29
影响因子：
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作者：
Wayne Rossman;Masaaki Umehara;Kotaro Yamada
通讯作者：
Kotaro Yamada