ABSTRACT
We undertake a more detailed study of minimal surfaces in this chapter. It builds on the theory of complex functions of one variable, the basics of which we take for granted. The concept of minimal isothermal patch, previously introduced in Section 16.7, allows us to start the present chapter by associating to a conjugate harmonic pair of patches an isometric deformation of minimal surfaces. The terminology of complex derivatives in Section 22.2 leads to the central notion of minimal curve in Section 22.3, and a simple algebraic method for constructing an isometric deformation from a minimal isothermal patch in Section 22.4.
