  This note is meant to introduce the reader to a duality principle for
nonlinear equations that recently appeared in the literature. Motivations come
from the desire to give a unifying potential-theoretic framework for various
maximum principles at infinity appearing in the literature (Ekeland, Omori-Yau,
Pigola-Rigoli-Setti), as well as to describe their interplay with properties
coming from stochastic analysis on manifolds. The duality involves an
appropriate version of these principles formulated for viscosity subsolutions
of fully nonlinear inequalities, called the Ahlfors property, and the existence
of suitable exhaustion functions called Khas'minskii potentials. We discuss
applications, also involving the geometry of submanifolds, in the last
sections, as well as the stability of these maximum principles when we remove
polar sets.
