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arXiv · 2206.02938

Unstable minimal surfaces in $\mathbb{R}^n$ and in products of hyperbolic surfaces

Vladimir Markovic·Nathaniel Sagman·Peter Smillie
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Abstract

We prove that every unstable equivariant minimal surface in $\mathbb{R}^n$ produces a maximal representation of a surface group into $\prod_{i=1}^n\textrm{PSL}(2,\mathbb{R})$ together with an unstable minimal surface in the corresponding product of closed hyperbolic surfaces. To do so, we lift the surface in $\mathbb{R}^n$ to a surface in a product of $\mathbb{R}$-trees, then deform to a surface in a product of closed hyperbolic surfaces. We show that instability in one context implies instability in the other two.

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Vladimir Markovic, Nathaniel Sagman, Peter Smillie. 2022-06-06. Unstable minimal surfaces in $\mathbb{R}^n$ and in products of hyperbolic surfaces. https://arxiv.org/abs/2206.02938

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