Journal Fü R Die Reine Und Angewandte Mathematik Discrete Constant Mean Curvature Surfaces and Their Index
Journal Fü R Die Reine Und Angewandte Mathematik Discrete Constant Mean Curvature Surfaces and Their Index
复制标题
DOI：
--
复制
发表时间：
--
期刊：
影响因子：
--
通讯作者：
Konrad Polthier At Berlin;W. Rossman;Kobe
中科院分区：
文献类型：
--
作者：
Konrad Polthier At Berlin;W. Rossman;Kobe
我们用变分特征定义了三角化分段线性常平均曲率曲面。这些表面对于保持边界条件、简单结构和（在非最小情况下）表面一侧的体积的连续分段线性变化中的面积至关重要。然后，我们找到了完整例子的显式公式，例如离散最小链面和螺旋面。我们通过数值计算这些离散曲面的雅可比算子的谱，来研究不稳定极小曲面的指数。我们的数值估计证实了一些光滑最小表面指数的已知结果，并提供了有关其面积减少变化的额外信息。这里的方法与其他数值研究不同，因为我们在离散曲面上添加了几何解释。
We define triangulated piecewise linear constant mean curvature surfaces using a variational characterization. These surfaces are critical for area amongst continuous piecewise linear variations which preserve the boundary conditions, the simplicial structures, and (in the nonminimal case) the volume to one side of the surfaces. We then find explicit formulas for complete examples, such as discrete minimal catenoids and helicoids. We use these discrete surfaces to study the index of unstable minimal surfaces, by numerically evaluating the spectra of their Jacobi operators. Our numerical estimates confirm known results on the index of some smooth minimal surfaces, and provide additional information regarding their area-reducing variations. The approach here deviates from other numerical investigations in that we add geometric interpretation to the discrete surfaces.