Harry Rauch

Harry Ernest Rauch (9 November 1925 to 18 June 1979) was an American mathematician who worked on complex analysis and differential geometry. Born in Trenton, New Jersey, he earned his doctorate at Princeton University in 1948 under Salomon Bochner, spent two years as a visiting member of the Institute for Advanced Study, and later taught at Yeshiva University and at the Graduate School of the City University of New York. His research dealt with geodesics on manifolds, Riemann surfaces and theta functions. In the early 1950s he made fundamental progress on the quarter-pinched sphere conjecture, showing that a simply connected manifold whose sectional curvature is pinched closely enough to constant curvature must be homeomorphic to a sphere. That result opened the line of pinching theorems later sharpened by Wilhelm Klingenberg and by Marcel Berger and Klingenberg. The Rauch comparison theorem, proved in 1951, also carries his name.