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arXiv · 2412.20502

On the Gauss Map of Anisotropic Minimal Surfaces and applications to the Morse Index estimates

Toshimi Inoue
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Abstract

In the paper, we study the Gauss map of a completely immersed anisotropic minimal surface with respect to convex parametric integrand in $\mathbb{R}^3$. By a local analysis, we prove the discreteness of the critical set of the Gauss map of an anisotropic minimal surface. In particular, we may consider the Gauss map as a branched covering map from an anisotropic minimal surface to the unit sphere. As a consequence, we may obtain an upper and a lower estimate for the Morse index of an anisotropic minimal surface by applying some conformal geometric technics to the Gauss map.

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Toshimi Inoue. 2024-12-29. On the Gauss Map of Anisotropic Minimal Surfaces and applications to the Morse Index estimates. https://arxiv.org/abs/2412.20502

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