Karsten Grove

Karsten Grove (born before 1960) is a Danish-American mathematician who studies differential geometry and topology.

Grove studied mathematics at the University of Aarhus , with the candidate degree in 1971 (About closed geodetic tables, Danish) and the licentiate degree in 1974 (thesis: Condition "(C)" for the energy integral on certain path spaces and applications to the theory of geodesics) at Vagn Lundsgaard Hansen. He was a professor at the University of Maryland and is a professor at the University of Notre Dame (Rev. Howard J. Kenna Professor).

He deals with metric geometry, differential geometry, topology and geometric analysis.

In 1977 he proved a theorem of spheres with K. Shiohama without an upper bound for the curvature, but with a lower bound for the diameter. After Alan Weinstein (1967) and Jeff Cheeger gave finiteness theorems in the 1960s for the number of homotopy types of manifolds of dimension d with restriction of section curvature, volume and diameter, Grove and Petersen 1988 proved finiteness with lower bound for section curvature and volume and upper bound Limit for the diameter.

He was invited speaker at the 1990 International Congress of Mathematicians in Kyoto ( Metric and Topological Measurements on Manifolds ).

Fonts

with Hermann Karcher : How to conjugate -close group actions. ${\ displaystyle C ^ {1}}$ In: Mathematical Journal . Vol. 132, 1973, pp. 11-20 .
with Hermann Karcher, Ernst A. Ruh : Group actions and curvature. In: Inventiones Mathematicae . Vol. 23, 1974, pp. 31-48 .
with Katsuhiro Shiohama: A generalized sphere theorem. In: Annals of Mathematics . Vol. 106, No. 1, 1977, pp. 201-211, doi : 10.2307 / 1971164 .
with Detlef Gromoll : On metrics on all of whose geodesics are closed. ${\ displaystyle S ^ {2}}$ In: Inventiones Mathematicae. Vol. 65, 1981/1982, pp. 175-177 .
with Stephen Halperin : Contributions of rational homotopy theory to global problems in geometry. In: Publications Mathématiques de l'IHÉS. Vol. 56, 1982, pp. 171-177, ( online ).
Metric differential geometry. In: Vagn L. Hansen (Ed.): Differential Geometry. Proceedings of the Nordic Summer School held in Lyngby, Denmark, Jul. 29 – Aug. 9, 1985 (= Lecture Notes in Mathematics . 1263). Springer, Berlin et al. 1987, ISBN 3-540-18012-5 , pp. 171-227.
with Detlef Gromoll: A generalization of Berger's rigidity theorem for positively curved manifolds. In: Annales Scientifiques de l'École Normale Supérieure. Vol. 20, No. 2, 1987, pp. 227-239, doi : 10.24033 / asens.1530 .
with Peter Petersen: Bounding homotopy types by geometry. In: Annals of Mathematics . Vol. 128, No. 2, 1988, pp. 195-206, doi : 10.2307 / 1971439 .
with Peter Petersen, Jyh-Yang Wu: Geometric finiteness theorems via controlled topology. In: Inventiones Mathematicae. Vol. 99, 1990, pp. 205-213 .
Ramifications of the classical sphere theorem. In: Arthur L. Besse (ed.): Actes de la Table Ronde de Géométrie Différentielle en l'Honneur de Marcel Berger. Center International de Rencontres Mathématiques de Luminy (CIRM) Marseille (France) 12-18 June 1992 (= Collection SMF. Séminaires et Congrès. 1). Société Mathématique de France, Paris 1996, ISBN 2-85629-047-7 , pp. 363-376.
with Frederick Wilhelm: Metric constraints on exotic spheres via Alexandrov geometry. In: Journal for pure and applied mathematics . Vol. 487, 1997, pp. 201-217 .
with Peter Petersen A radius sphere theorem. In: Inventiones Mathematicae. Vol. 112, 1993, pp. 577-583 .
with Burkhard Wilking , Wolfgang Ziller: Positively curved cohomogeneity one manifolds and 3-Sasakian geometry. In: Journal of Differential Geometry . Vol. 78, No. 1, 2008, pp. 33-111, ( online ).
as editor with Peter Petersen: Comparison Geometry (= Mathematical Sciences Research Institute Publications. 30). Cambridge University Press, Cambridge et al. 1997, ISBN 0-521-59222-4 .
as editor with Ib Henning Madsen , Erik Kjær Pedersen: Geometry and Topology. Conference on Geometry and Topology, August 10-16, 1998, Aarhus University, Aarhus, Denmark (= Contemporary Mathematics . 258). American Mathematical Society, Providence RI 2000, ISBN 0-8218-2158-X .

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personal data
SURNAME	Grove, Karsten
BRIEF DESCRIPTION	Danish-American mathematician
DATE OF BIRTH	before 1960