In this thesis, we study the boundary-blow-up problem for the negative $sigma_k$-Ricci equations in bounded domains of R^n. By adopting the method of Loewner-Nirenberg for the scalar curvature, we generalize their results to the negative $sigma_k$-Ricci equations. When $k=1,2,$ and $n$, the necessary condition for the existence of the solutions satisfying the $sigma_k$-Ricci equations is that the codimension of the portion of boundary has to be bounded from above by some constants depending on $n$ and $k$. For other cases, we believe that the similar argument can be developed.