  We study the good shape property of boundary sections of convex solutions of
the oblique boundary value problem for Monge-Amp\`ere equations $$\det D^2u
=f(x) \text{ in } \Omega , \quad D_{\beta}u = \phi(x) \text{ on } \partial
\Omega.$$ In the two-dimensional case, we prove the global $C^{2,\alpha}$
estimate for the solution. When the dimension $n \geq 3$, we show that this
estimate still holds if the solution is bounded from above by a quadratic
function in the tangent direction. We also obtain an existence result for the
convex solution of Monge-Amp\`ere equations with Robin oblique boundary
conditions.
