The well-known Cartan-Hadamard conjecture states that the classical isoperimetric inequality for domains in Euclidean space can be generalized to manifolds of nonpositive curvature. It is also known that this conjecture would follow from an estimate for total curvature of convex hypersurfaces. Motivated by these problems, we develop in this talk a comparison formula for total curvature of level sets of functions in Riemannian manifolds, and discuss some of its applications. This is joint work with Joel Spruck.