Minimal surfaces in 3-d Euclidean space and maximal surfaces in 3-d Lorentz Minkowski space are defined to be zero mean curvature surfaces. The general solutions are given by the Weierstrass-Enneper representations of these surfaces.We will first re- derive the Weierstrass-Enneper representation of a minimal surface using hodographic coordinates which was first introduced in the context of solitons by Barbishov and Chernikov. We will mention an interesting link between minimal surfaces and Born-Infeld solitons. Next we will talk about some identities we obtain from certain Ramanujan's identities and their link with some of these surfaces. This link was first studied by Randall Kamien et al in the context of liquid crystals. If time permits, we will introduce maximal surfaces in Lorentzian space and talk about analogous results.
Please note that the talk will be very elementary.