Journal of Differential Geometry

On the topology and index of minimal surfaces

Otis Chodosh and Davi Maximo

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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.

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J. Differential Geom., Volume 104, Number 3 (2016), 399-418.

Received: 30 September 2014
First available in Project Euclid: 3 November 2016

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Chodosh, Otis; Maximo, Davi. On the topology and index of minimal surfaces. J. Differential Geom. 104 (2016), no. 3, 399--418. doi:10.4310/jdg/1478138547.

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