Minimal surfaces and the new main inequality

We establish the new main inequality as a minimizing criterion for minimal maps into products of \(R\)-trees, and the infinitesimal new main inequality as a stability criterion for minimal maps to \(R^n\). Along the way, we develop a new perspective on destabilizing minimal surfaces in \(R^n\), and as a consequence we reprove the instability of some classical minimal surfaces; for example, the Enneper surface.