There are many examples of minimal functions/surfaces throught internet (Minimal Surfaces -- from Wolfram MathWorld). And i even found smth like parametrization of ALL minimal surfaces (Minimal Surface -- from Wolfram MathWorld). But i cannot get properties of such space of minimal functions. As, let say, subspace of integrable functions in $\displaystyle R^2$. I'm interest in next questions. Will be this space infinite-dimensional (it's trivial, yes - there are many pairs of analytic and meromorphic functions).

Will it be connected in topological space?