  In this paper, we study the motion of level sets by general curvature. The
difficulty of this setting is that a general curvature function is only well
defined in an admissible cone. In order to extend the existence of a weak
solution of a general curvature flow to outside the cone we introduce a new
approximation function $\hat{f}^n$ (see (3.1)). Moreover, using the idea in
[4], we give an elliptic approach for the Ben-Andrews' non-collapsing result in
fully nonlinear curvature flows; we hope this approach can be generalized to a
wider class of elliptic equations.
