The Weyl problem with nonnegative Gauss curvature in hyperbolic space
  In this paper, we discuss the isometric embedding problem in hyperbolic space with nonnegative extrinsic curvature. We prove a priori bounds for the trace of the second fundamental form H and extend the result to n-dimensions. We also obtain an estimate for the gradient of the smaller principal curvature in 2 dimensions. 
Jui-En Chang and Ling Xiao
math.DG