Curvature estimates for minimal surfaces with total boundary curvature less than 4pi
Curvature estimates for minimal surfaces with total boundary curvature less than 4pi
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总边界曲率小于 4pi 的最小曲面的曲率估计
DOI：
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发表时间：
2007
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：
G. Tinaglia
我们建立了总边界曲率小于 4π 的经典最小曲面的曲率估计。主要应用是仅取决于边界曲线的几何形状对这些曲面的约束。我们还证明，对于任何给定的 g，总曲率小于 4π 且不限制大于 g 的可定向紧嵌入最小曲面的简单闭合曲线集在 C 2,α 拓扑中是开集。
We establish a curvature estimate for classical minimal surfaces with total boundary curvature less than 4π. The main application is a bound on the genus of these surfaces depending solely on the geometry of the boundary curve. We also prove that the set of simple closed curves with total curvature less than 4π and which do not bound an orientable compact embedded minimal surface of genus greater than g, for any given g, is open in the C 2,α topology.