  We present a self-contained treatment of the fundamental role that
quasi-convex functions play in general (nonlinear second order) potential
theories, which concerns the study of generalized subharmonics associated to a
suitable closed subset (subequations) of the space of 2-jets. Quasi-convex
functions build a bridge between classical and viscosity notions of solutions
of the natural Dirichlet problem in any potential theory. Moreover, following a
program initiated by Harvey and Lawson in [arXiv:0710.3991], a
potential-theoretic approach is widely being applied for treating nonlinear
partial differential equations (PDEs). This viewpoint revisits the conventional
viscosity approach to nonlinear PDEs [arXiv:math/9207212] under a more
geometric prospective inspired by Krylov (1995) and takes much insight from
classical pluripotential theory. The possibility of a symbiotic and productive
relationship between general potential theories and nonlinear PDEs relies
heavily on the class of quasi-convex functions, which are themselves the
generalized subharmonics of a pure second order constant coefficient potential
theory.
