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}\mathrm{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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