Keywords

• minimal surface
• conformal parametrization
• quaternionic factorization

Abstract I will present a quaternionic description of minimal surfaces in conformal parametrization. In the classical setting, minimal surfaces arise from holomorphic null curves through the Weierstrass-Enneper representation. The key observation is that the nullity condition can be encoded very compactly using complexified quaternions, in the form

This viewpoint makes the underlying algebraic structure explicit and reveals a natural analogy with Pythagorean-hodograph curves, where quaternionic factorizations also play a central role. I will discuss some standard examples and briefly explain the appearance of Sylvester-type equations in explicit computations.