The Diederich–Fornaess index and Steinness index

We shall explain formulae that express two indices in the title, which are defined for bounded pseudoconvex domains in complex manifolds and measure how well their boundaries are approximated by s.p.c. real hypersurfaces. Our formulae involve not only Levi form of the boundary but also d'Angelo 1-form and work for Takeuchi 1-convex domains in arbitrary complex manifolds. This is a joint work with Jihun Yum in Pusan National University, South Korea.