On the four vertex theorem for curves on locally convex surfaces

The classical four vertex theorem describes a fundamental property of simple closed planar curves. It has been extended to space curves, namely a smooth, simple closed curve in R3 has at least four points with vanishing torsion if it lies on a convex surface. More recently, Ghomi [6] extended this property to curves lying on locally convex surfaces. In this paper we provide an alternative approach to the result via the theory of Monge-Ampere equations.