Frank Wilson Warner III (born March 2 1938 in Pittsfield, Massachusetts)[1] is an American mathematician, specializing in differential geometry.
Warner graduated in 1959 with a bachelor's degree from Pennsylvania State University and in 1963 with a Ph.D. in mathematics from the Massachusetts Institute of Technology.
His thesis, written under the supervision of Isadore M. Singer, is entitled Conjugate Locus of a Riemannian Manifold.
[3] In the 1970s he and Jerry Kazdan, as collaborators, made important contributions to the theory of Riemannian manifolds with prescribed scalar curvature.
They proved in 1975 that any smooth function can be realized as a scalar curvature if it becomes negative somewhere on the manifold.