Background
He was born in Trenton, New Jersey, and died in White Plains, New New York
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Harry Rauch
Edit Profilemathematician university professor
Education
Rauch earned his Doctor of Philosophy in 1948 from Princeton University under Salomon Bochner with thesis Generalizations of Some Classic Theorems to the Case of Functions of Several Variables.
Career
He was in the 1960s a professor at Yeshiva University and from the mid-1970s a professor at the City University of New New York His research was on differential geometry (especially geodesics on n-dimensional manifolds), Riemann surfaces, and theta functions. In the early 1950s Rauch made fundamental progress on the quarter-pinched sphere conjecture in differential geometry.
Rauch"s result created a new paradigm in differential geometry, that of a "pinching theorem;" in Rauch"s case, the assumption was that the curvature was pinched between 0.76 and 1.
This was latter relaxed to pinching between 0.55 and 1 by Wilhelm Klingenberg, and finally replaced with the sharp result of pinching between 0.25 and 1 by Marcel Berger and Klingenberg in the early 1960s. This optimal result is known as the sphere theorem for Riemannian manifolds.
The Rauch comparison theorem is also named after Harry Rauch. He proved it in 1953.
Membership
From 1949 to 1951 he was a visiting member of the Institute for Advanced Study.
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Born
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Died
June 18, 1979 (aged 53) -
Nationality
United States