André Neves

André Neves, together with several collaborators, has solved some fundamental problems involving the geometry of surfaces. For example, with Fernando Marquez, he has proved that the least bended torus in space is the Clifford torus and, in so doing, solved the Willmore conjecture. The method of proof was quite surprising. It used the theory of unstable minimal surfaces, or min-max theory, which seemed to have nothing to do with the Willmore conjecture. Using additional min-max arguments, again, together with Fernando Marquez, he showed that any compact manifold that is positively curved has an infinite number of minimal hypersurfaces. For this discovery, Neves and Marques won the 2016 Oswald Veblen Prize in Geometry from the American Math Society.