The Koppelman-Leray- Norguet formula of type (p,q) on Stein manifolds

Abstract:

      Let M be a Stein manifold of complex dimension n,and let an open set D??M have a piecewise C¹-boundary. Using Chern metric and connection, we obtain an integral representation of (p, q) differential forms on D, which is a generali-zation of the Koppelman-Leray-Norgeut formula for (0,q)-forms on Stein mani-folds. A integral formula for solving the ?-equation on D is also obtained. Finally, a formula for real non-degenerate strictly pseudoconvex polyhedron is given .