  We establish a concavity principle for solutions to elliptic and parabolic
equations on complex projective space, generalizing the results of Langford and
Scheuer. To our knowledge, this is the first example of a general concavity
principle outside the constant sectional curvature regime, and in particular,
our result partially answers a question raised by Korevaar in 1985 regarding
the concavity of solutions to elliptic equations on manifolds with non-constant
sectional curvature.
