Abstract
A super-conformal map and a minimal surface are factored into a product of two maps by modeling the Euclidean four-space and the complex Euclidean plane on the set of all quaternions. One of these two maps is a holomorphic map or a meromorphic map. These conformal maps adopt properties of a holomorphic function or a meromorphic function. Analogs of the Liouville theorem, the Schwarz lemma, the Schwarz-Pick theorem, the Weierstrass factorization theorem, the Abel-Jacobi theorem, and a relation between zeros of a minimal surface and branch points of a super-conformal map are obtained.
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Moriya, K. A factorization of a super-conformal map. Isr. J. Math. 207, 331–359 (2015). https://doi.org/10.1007/s11856-015-1176-6
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DOI: https://doi.org/10.1007/s11856-015-1176-6