  This paper considers asymptotically hyperbolic manifolds with a finite
boundary intersecting the usual infinite boundary -- cornered asymptotically
hyperbolic manifolds -- and proves a theorem of Cartan-Hadamard type near
infinity for the normal exponential map on the finite boundary. As a main
application, a normal form for such manifolds at the corner is then
constructed, analogous to the normal form for usual asymptotically hyperbolic
manifolds and suited to studying geometry at the corner. The normal form is at
the same time a submanifold normal form near the finite boundary and an
asymptotically hyperbolic normal form near the infinite boundary.
