On a problem of Moser

1 0 Introduction This paper studies the analytic structure of the local hull of holomorphy of a 2-dimensional, real analytic manifold that is embedded in C 2. Our specific purpose is to solve a problem of Jurgen Moser (see [MOS], [MOW]). [In the statement of this problem we shall use certain standard terminology from the literature that will be defined later.] The result is: THEOREM 0.1 Let M be a 2-dimensional, real analytic embedded submanifold of C 2. Suppose that z 0 ∈ M is a non-degenerate elliptic point of M. Then the local hull of holomorphy M of M near z 0 is a Levi flat hypersurface which is real analytic across the boundary manifold M. Recall that for a general closed subset E ⊆ C n , we define here the hull of holomorphy E of E to be the intersection of all Stein neighborhoods of E.