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is homeomorphic to a sphere. Subsequently, the critical point theory for distance functions developed as part of the proof of this result led to several important advances in the area. Another result obtained by Grove, in collaboration with Peter
Petersen, is the
84:, where he obtained a Cand. Scient. (equivalent to a M.A.) in 1971 and Lic. Scient. (equivalent to a Ph.D.) in 1974. Between 1971 and 1972 he also acted as an instructor at Aarhus University. From 1972 to 1974 he had a postdoctoral position at the
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in 1984, retiring from this position in 2009. Since 2007 he has held the endowed chair of "Rev. Howard J. Kenna, C.S.C. Professor" at the
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Danish-American mathematician
Karsten Grove at Berkeley, California; headshot portion re-scanned with increased resolution
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of manifolds of a fixed dimension with lower sectional curvature bounds, upper diameter bound, and lower volume bound.
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One of Grove's most recognized mathematical contributions to
Riemannian Geometry is the
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Grove, Karsten; Petersen, Peter (1988-01-01). "Bounding homotopy types by geometry".
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Grove, Karsten; Shiohama, Katsuhiro (1977-01-01). "A generalized sphere theorem".
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