  We study the exact effect of the anisotropic convexity of domains on the
boundary estimate for two Monge-Amp\`ere Equations: one is singular which is
from the proper affine hyperspheres with constant mean curvature; the other is
degenerate which is from the Monge-Amp\`ere eigenvalue problem. As a result, we
obtain the sharp boundary boundary estimates and the optimal global H\"older
regularity for the two equations.
