The Propeller: A Counterexample to a Conjectured Criterion for the Existence of Certain Convex Functions
Wilfrid S. Kendall · Journal of the London Mathematical Society · 1992
A counterexample is given to a conjecture by Emery; it is shown how to construct a domain B (the ‘propeller’) of a two-dimensional Riemannian manifold such that any pair of points in B is connected by one and only one geodesic in B and yet there is no convex function L:B × B → [0, 1] vanishing only on the diagonal of B × B.