  For a class of competitive maps there is an invariant one-codimensional
manifold (the carrying simplex) attracting all non-trivial orbits. In the
present paper it is shown that its convexity implies that it is a $C^1$
submanifold-with-corners, neatly embedded in the non-negative orthant. The
proof uses the characterization of neat embedding in terms of inequalities
between Lyapunov exponents for ergodic invariant measures supported on the
boundary of the carrying simplex.
