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arXiv · 2309.05742

On the topology and index of minimal/Bryant framed surfaces

Davi Maximo·Franco Vargas Pallete
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Abstract

We study framed surfaces, which are a class of Euclidean minimal and hyperbolic CMC-1 surfaces that generalize immersed minimal surfaces in $\mathbb{R}^3$ and Bryant surfaces. For this class we prove a lower bound on the (unrestricted) Morse index by a linear function of the genus, number of ends and number of branch points (counting multiplicity), generalizing a result by Chodosh and the first author. We include as well a description of the 1-to-1 correspondence between Euclidean minimal and Bryant surfaces, known in the literature as Lawson's correspondence.

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Davi Maximo, Franco Vargas Pallete. 2023-09-11. On the topology and index of minimal/Bryant framed surfaces. https://arxiv.org/abs/2309.05742

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