On the topology and index of minimal surfaces II
On the topology and index of minimal surfaces II
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DOI：
10.4310/jdg/1478138547
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发表时间：
2014-05
影响因子：
2.5
通讯作者：
Otis Chodosh;Davi Máximo
中科院分区：
文献类型：
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作者：
Otis Chodosh;Davi Máximo
我们表明，浸入双边极小曲面在R 3中，有一个下界的指数依赖于亏格和数量的结束。利用这一点，我们证明了不存在嵌入极小曲面在R 3的指数为2，作为证明由Choe（Cho90）。此外，我们证明了一个浸入的双边极小曲面与嵌入端的指数是有界的从上到下的曲面的总曲率的线性函数。
We show that for an immersed two-sided minimal surface in R 3 , there is a lower bound on the index depending on the genus and number of ends. Using this, we show the nonexistence of an embedded minimal surface in R 3 of index 2, as conjectured by Choe (Cho90). Moreover, we show that the index of an immersed two-sided minimal surface with embedded ends is bounded from above and below by a linear function of the total curvature of the surface.