A factorization of a super-conformal map (Q2351750)

Let \(M\) be a Riemannian surface and \(\mathbb{H}\) be the set of quaternions. A conformal map \(f:M\rightarrow \mathbb{H}\) is said to be super-conformal if its curvature ellipse is a circle. In this paper, the author provides a factorization theorem for super-conformal maps and, also, a factorization theorem for minimal surfaces. Using the factorization theorem for super-conformal maps, the author derives some interesting results, like Liouville's theorem, the Schwarz lemma, the Schwarz-Pick theorem, the geometric version of the Schwarz-Pick theorem, the Weierstraß factorization theorem and the Abel-Jacobi theorem for super-conformal maps. Moreover, in the last part of the paper, the author obtains a relation between zeros of a minimal surface and branch points of a super-conformal map.