The dynamics theorem for CMC surfaces in R^3
The dynamics theorem for CMC surfaces in R^3
复制标题
R^3 中 CMC 表面的动力学定理
DOI：
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发表时间：
2008
期刊：
影响因子：
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通讯作者：
G. Tinaglia
中科院分区：
文献类型：
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作者：
W. Meeks;G. Tinaglia
本文研究具有非零常平均曲率和有界第二基本形式的曲面M适当嵌入R^3的平移极限空间T(M)。存在赋给T(M)中任意曲面M‘的自然映射T，T(M)中的集合T(M’)。在各种动力学类型的结果中，我们证明了T(M)的极小T-不变集上的曲面是弦弧的。我们还证明了如果M有无穷多个端点，则T(M)中存在一个非空的极小T-不变集，它完全由具有Alexandrov对称平面的曲面组成。最后，当M具有Alexandrov对称性的平面时，我们证明了下面的特征定理：M有有限拓扑当且仅当M有有限个大于1的端数。
In this paper, we study the space of translational limits T(M) of a surface M properly embedded in R^3 with nonzero constant mean curvature and bounded second fundamental form. There is a natural map T which assigns to any surface M' in T(M), the set T(M') in T(M). Among various dynamics type results we prove that surfaces in minimal T-invariant sets of T(M) are chord-arc. We also show that if M has an infinite number of ends, then there exists a nonempty minimal T-invariant set in T(M) consisting entirely of surfaces with planes of Alexandrov symmetry. Finally, when M has a plane of Alexandrov symmetry, we prove the following characterization theorem: M has finite topology if and only if M has a finite number of ends greater than one.
影响因子：
0.9
作者：
Smyth B
通讯作者：
Smyth B