Structure theorems for constant mean curvature surfaces bounded by a planar curve
Structure theorems for constant mean curvature surfaces bounded by a planar curve
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由平面曲线界定的恒定平均曲率表面的结构定理
DOI：
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发表时间：
1991
影响因子：
1.1
通讯作者：
W. H.
中科院分区：
文献类型：
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作者：
Samuel W. F. Earp;Ricardo Brito;Fabiano Meeks;W. H.
证明了R3中边界为圆的紧致连通嵌入常平均曲率曲面一定是球面的一部分，并假定该曲面沿边界圆与该圆的平面横向相交.这一证明依赖于A.D.Alexandrov的平面反射fl技术和力平衡恒等式，该恒定平均曲率曲面也成立。
The authors prove that a compact, connected, embedded, constant mean curvature surface in R 3 whose boundary is a circle must be part of a sphere, under the additional hypothesis that along the boundary circle the surface meet the plane of the circle transversely. The proof relies on the plane-reflection technique of A. D. Alexandrov and on the force-balancing identity which holds for pieces of constant mean curvature surfaces.