  In this paper, a supersymmetric extension of the minimal surface equation is
formulated. Based on this formulation, a Lie superalgebra of infinitesimal
symmetries of this equation is determined. A classification of the
one-dimensional subalgebras is performed, which results in a list of 143
conjugacy classes with respect to action by the supergroup generated by the Lie
superalgebra. The symmetry reduction method is used to obtain invariant
solutions of the supersymmetric minimal surface equation. The classical minimal
surface equation is also examined and its group-theoretical properties are
compared with those of the supersymmetric version.
