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arXiv · 2103.10588

On the index of minimal surfaces with free boundary in a half-space

Shuli Chen
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Abstract

We study the Morse index of minimal surfaces with free boundary in a half-space. We improve previous estimates relating the Neumann index to the Dirichlet index and use this to answer a question of Ambrozio, Buzano, Carlotto, and Sharp concerning the non-existence of index two embedded minimal surfaces with free boundary in a half-space. We also give a simplified proof of a result of Chodosh and Maximo concerning lower bounds for the index of the Costa deformation family.

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Shuli Chen. 2021-03-19. On the index of minimal surfaces with free boundary in a half-space. https://arxiv.org/abs/2103.10588

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