  We prove the concavity of classical solutions to a wide class of degenerate
elliptic differential equations on strictly convex domains of the unit sphere.
The proof employs a suitable two-point maximum principle, a technique which
originates in works of Korevaar, Kawohl and Kennington for equations on
Euclidean domains. We emphasize that no differentiability of the differential
operator is needed, but only some monotonicity and concavity properties.
