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- Harry_Rauch abstract "Harry Ernest Rauch (November 9, 1925 – June 18, 1979) was an American mathematician, who worked on complex analysis and differential geometry. He was born in Trenton, New Jersey, and died in White Plains, New York.Rauch earned his PhD in 1948 from Princeton University under Salomon Bochner with thesis Generalizations of Some Classic Theorems to the Case of Functions of Several Variables. From 1949 to 1951 he was a visiting member of the Institute for Advanced Study. He was in the 1960s a professor at Yeshiva University and from the mid-1970s a professor at the City University of 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. In the case of positive sectional curvature and simply connected differential manifolds, Rauch proved that, under the condition that the sectional curvature K does not deviate too much from K = 1, the manifold must be homeomorphic to the sphere (i.e. the case where there is constant sectional curvature K = 1). Rauch's result created a new paradigm in differential geometry, that of a \"pinching theorem;\" in Rauch's case, the assumption was that the curvaturewas 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 1by 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.".
- Harry_Rauch birthDate "1925-11-09".
- Harry_Rauch birthYear "1925".
- Harry_Rauch deathDate "1979-06-18".
- Harry_Rauch deathYear "1979".
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- Harry_Rauch wikiPageWikiLink Category:20th-century_American_mathematicians.
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- Harry_Rauch wikiPageWikiLink Category:Differential_geometers.
- Harry_Rauch wikiPageWikiLink Category:People_from_Trenton,_New_Jersey.
- Harry_Rauch wikiPageWikiLink Category:Princeton_University_alumni.
- Harry_Rauch wikiPageWikiLink Category:Yeshiva_University_faculty.
- Harry_Rauch wikiPageWikiLink City_University_of_New_York.
- Harry_Rauch wikiPageWikiLink Complex_analysis.
- Harry_Rauch wikiPageWikiLink Differential_geometry.
- Harry_Rauch wikiPageWikiLink Geodesic.
- Harry_Rauch wikiPageWikiLink Institute_for_Advanced_Study.
- Harry_Rauch wikiPageWikiLink Marcel_Berger.
- Harry_Rauch wikiPageWikiLink Princeton_University.
- Harry_Rauch wikiPageWikiLink Rauch_comparison_theorem.
- Harry_Rauch wikiPageWikiLink Riemann_surface.
- Harry_Rauch wikiPageWikiLink Salomon_Bochner.
- Harry_Rauch wikiPageWikiLink Sectional_curvature.
- Harry_Rauch wikiPageWikiLink Sphere_theorem.
- Harry_Rauch wikiPageWikiLink Theta_function.
- Harry_Rauch wikiPageWikiLink Trenton,_New_Jersey.
- Harry_Rauch wikiPageWikiLink White_Plains,_New_York.
- Harry_Rauch wikiPageWikiLink Wilhelm_Klingenberg.
- Harry_Rauch wikiPageWikiLink Yeshiva_University.
- Harry_Rauch wikiPageWikiLinkText "Harry Rauch".
- Harry_Rauch wikiPageWikiLinkText "Rauch, Harry".
- Harry_Rauch dateOfBirth "1925-11-09".
- Harry_Rauch dateOfDeath "1979-06-18".
- Harry_Rauch id "8108".
- Harry_Rauch name "Harry Ernest Rauch".
- Harry_Rauch name "Rauch, Harry".
- Harry_Rauch shortDescription "American mathematician".
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- Harry_Rauch description "American mathematician".
- Harry_Rauch description "American mathematician".
- Harry_Rauch subject Category:1925_births.
- Harry_Rauch subject Category:1979_deaths.
- Harry_Rauch subject Category:20th-century_American_mathematicians.
- Harry_Rauch subject Category:City_University_of_New_York_faculty.
- Harry_Rauch subject Category:Differential_geometers.
- Harry_Rauch subject Category:People_from_Trenton,_New_Jersey.
- Harry_Rauch subject Category:Princeton_University_alumni.
- Harry_Rauch subject Category:Yeshiva_University_faculty.
- Harry_Rauch hypernym Mathematician.
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- Harry_Rauch comment "Harry Ernest Rauch (November 9, 1925 – June 18, 1979) was an American mathematician, who worked on complex analysis and differential geometry. He was born in Trenton, New Jersey, and died in White Plains, New York.Rauch earned his PhD in 1948 from Princeton University under Salomon Bochner with thesis Generalizations of Some Classic Theorems to the Case of Functions of Several Variables. From 1949 to 1951 he was a visiting member of the Institute for Advanced Study.".
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- Harry_Rauch name "Harry Rauch".
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