POSITIVELY CURVED SURFACES WITH NO TANGENT SUPPORT PLANE

JOHN MCCUAN

Abstract. We discuss a characterization of positively curved surfaces M with the property that at each point the tangent plane to M is not a support plane for the entire surface. A one parameter family of examples which have special relevance with respect to the characterization is also given. Each member of this family is a smooth embedded surface in ℝ^{3} that is topologically a disk, has everywhere positive Gauss curvature, but has none of its tangent planes as a support plane.