  We address the restriction problem for viscosity subsolutions of a fully
nonlinear PDE on a manifold Z. The constraints on the restrictions of smooth
subsolutions to a submanifold X in Z determine a restricted subequation on X.
The problem is to show that general (upper semi-continuous) subsolutions
restrict to satisfy the same constraints. We first prove an elementary result
which, in theory, can be applied to any subequation. Then two definitive
results are obtained. The first applies to any "geometrically defined"
subequation, and the second to any subequation which can be transformed to a
constant coefficient (i.e., euclidean) model. This provides a long list of
geometrically and analytically interesting cases where restriction holds.
