Hans Werner Ballmann
Hans Werner Ballmann (born 11 April 1951) is a German mathematician who is engaged in differential geometry and global analysis.
Life
Werner Ballmann studied mathematics at the University of Bonn. In 1976, he earned his diploma in 1979, he was with Wilhelm Klingenberg doctorate (Some new results on manifolds not positive curvature ). He was then a research assistant there, habilitated there in 1984, was in 1980/81 as a post- doctoral student at the University of Pennsylvania and from 1984 Associate Professor at the University of Maryland. In 1986 he became a professor in Bonn and in 1987 at the University of Zurich. In 1989 he took over the Chair of Differential Geometry by Prof. Dr. Wilhelm Klingenberg at the Rheinische Friedrich -Wilhelms University in Bonn, where he still teaches. Several times he was executive director of the Mathematical Institute. 1996-99 he was Speaker of the Collaborative Research Centre 256 Nonlinear partial differential equations. Since 2007 Werner Ballmann is Director at the Max Planck Institute for Mathematics. Since 2009 he is the coordinator of the Hausdorff Center for Mathematics and board member of the Institut des Hautes Études Scientifiques.
In 1986 he was invited speaker at the International Congress of Mathematicians in Berkeley ( Manifolds of non positive sectional curvature and manifolds without conjugate points). Since 2007 he is a member of the Leopoldina. Since 2004 he has been in the Council of the Mathematical Research Institute Oberwolfach.
His doctoral include Christian Bär, Vicente Cortés, Alexander Lytchak, Dorothee Schüth, Gregor Weingart and Anna Vienna Hard.
Work
Ballmann engaged in differential geometry and global analysis. Among other things he examined closed geodesic structure of non- positive curvature areas and applications in the geometric group theory, the Laplace equation with Dirichlet boundary conditions at infinity on areas of non- positive curvature, and the spectrum of Diracoperatoren. One of his main results is the so -called rank rigidity theorem, see Ann. of Math 122 (1985), pp. 597-609. This theorem states that a complete Riemannian manifold of non- positive curvature and finite volume limited by the rank at least 2 is a symmetric space or a product locally.
Writings
- Lectures on spaces of non positive curvatures (PDF, 818 kB), DMV Seminar, Birkhäuser 1995
- Spaces of non positive curvature, DMV Annual Report, Volume 103, 2001, pp. 52-65
- The set of Lusternik and Schnirelmann, Bonner Mathematische Schriften, Volume 102, 1978, p 1-25
- With G. Thorbergsson and W. Ziller, Closed geodesics on positively curved manifolds, Ann. of Math 116 (1982), pp. 213-247
- Nonpositively curved manifolds of higher rank, Ann. of Math 122 (1985), pp. 597-609
- With M. Brin: Orbihedra of nonpositive curvature. Inst Hautes Études Sci. Publ Math No. 82 (1995), 169-209 (1996).
- With J. Swiatkowski: On- cohomology and property (T) for automorphism groups of polyhedral cell complexes. Geom Funct. Anal. 7 (1997 ), no 4, 615-645.