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arXiv · 1405.7356

On the topology and index of minimal surfaces

Otis Chodosh·Davi Maximo
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Abstract

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. Moreover, we show that the index of a 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.

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Otis Chodosh, Davi Maximo. 2014-05-28. On the topology and index of minimal surfaces. https://doi.org/10.4310/jdg/1478138547

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