A branched minimal immersion from C to R^n is stable if and only if it lies in an even-dimensional affine subspace and is holomorphic for some orthogonal complex structure.
Unstable minimal surfaces inR n and in products of hyperbolic surfaces.Commentarii Mathematici Helvetici, 100:93–121
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Holomorphicity of stable minimal surfaces of low genus
A branched minimal immersion from C to R^n is stable if and only if it lies in an even-dimensional affine subspace and is holomorphic for some orthogonal complex structure.