Abstract
We show that for an immersed two-sided minimal surface in $\mathbb{R}^3$, 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 $\mathbb{R}^3$ of index $2$, as conjectured by Choe. 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.
Citation
Otis Chodosh. Davi Maximo. "On the topology and index of minimal surfaces." J. Differential Geom. 104 (3) 399 - 418, November 2016. https://doi.org/10.4310/jdg/1478138547
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