We prove that isospectral simple analytic surfaces of revolution are isometric. 0 Introduction This article is concerned with the inverse spectral problem for metrics of revolution on S. We will assume that our metrics are real analytic and belong to a class R∗ of rotationally invariant metrics which are of ‘simple type’ and which satisfy some generic non-degeneracy conditions (see Definition (0.1)). In particular, we will assume they satisfy the generalized ‘simple length spectrum’ condition… CONTINUE READING