  This is an essay on potential theory for geometric plurisubharmonic
functions. It begins with a given closed subset G of the Grassmann bundle
$G(p,TX)$ of tangent $p$-planes to a riemannian manifold $X$. This determines a
nonlinear partial differential equation which is convex but never uniformly
elliptic (p < dim X). A surprising number of results in complex analysis carry
over to this more general setting. The notions of: a G-submanifold, an upper
semi-continuous G-plurisubharmonic function, a G-convex domain, a G-harmonic
function, and a G-free submanifold, are defined. Results include a restriction
theorem as well as the existence and uniqueness of solutions to the Dirichlet
Problem for G-harmonic functions on G-convex domains.
