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ON ALGEBRAIC MINIMAL SURFACES IN ℝ3 DERIVING FROM CHARGE 2 MONOPOLE SPECTRAL CURVES
Preview AbstractWe give formulae for minimal surfaces in ℝ3 deriving, via classical osculation duality, from elliptic curves in a line bundle over ℙ1. Specialising to the case of charge 2 monopole spectral curves we find that the distribution of Gaussian curvature on the auxiliary minimal surface reflects the monopole's structure. This is elucidated by the behaviour of the surface's Gauss map.