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We present a self-contained introduction to the fundamental role thatquasi-convex functions play in general (nonlinear second order) potentialtheories, which concerns the study of generalized subharmonics associated to asuitable closed subset of the space of 2-jets. Quasi-convex functions build abridge between classical and viscosity notions of solutions of the naturalDirichlet problem in any potential theory. Moreover, following a programinitiated by Harvey and Lawson in 2009, a potential theoretic-approach iswidely being applied for treating nonlinear partial differential equations(PDEs). This viewpoint revisits the conventional viscosity approach tononlinear PDEs under a more geometric prospective inspired by Krylov and takesmuch insight from classical pluripotential theory. The possibility of asymbiotic and productive relationship between general potential theories andnonlinear PDEs relies heavily on the class of quasi-convex functions, which arethemselves the protagonists of a particular (and important) pure second orderpotential theory.

A primer on quasi-convex functions in nonlinear potential theories