  Consider the steady neutron transport equation with diffusive boundary
condition. In [Wu and Guo(2015) Comm. Math. Phys.] and [Wu and Yang and
Guo(2016) Preprint], it was discovered that geometric correction is necessary
for the Milne problem of Knudsen-layer construction in a disk or annulus. In
this paper, we establish diffusive limit for a 2D convex domain. Our
contribution relies on novel $W^{1,\infty}$ estimates for the Milne problem
with geometric correction in the presence of a convex domain, as well as an
$L^{2m}-L^{\infty}$ framework which yields stronger remainder estimates.
