Minimal surfaces and the new main inequality

Abstract

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