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November 2016 On the topology and index of minimal surfaces
Otis Chodosh, Davi Maximo
J. Differential Geom. 104(3): 399-418 (November 2016). DOI: 10.4310/jdg/1478138547

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.

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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

Information

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

zbMATH: 1357.53016
MathSciNet: MR3568626
Digital Object Identifier: 10.4310/jdg/1478138547

Rights: Copyright © 2016 Lehigh University

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Vol.104 • No. 3 • November 2016
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