Profile
Profile

Prof. Dr. Werner Ballmann

E-mail: hwbllmnn(at)mpim-bonn.mpg.de
Phone: +49 228 402240
Fax: +49 228 73 62268
Homepage: http://www.mpim-bonn.mpg.de/node/103
Room: 214
Location: Max-Planck-Institute for Mathematics
Institute: Max-Planck-Institute for Mathematics
Mathematical Institute
Research Areas: Research Area A
Research Area G (until 10/2012)
Former Research Area F
Birthdate: 11.Apr 1951
Mathscinet-Number: 30135

Academic Career

1979

Dr. rer. nat., University of Bonn

1979 - 1985

Assistant Professor, University of Bonn

1984 - 1986

Associate Professor, University of Maryland, College Park, MD, USA

1986 - 1987

Professor (C3), University of Bonn

1987 - 1989

Ordinarius, University of Zürich, Switzerland

1989 - 2016

Professor (C4), University of Bonn

Since 2007

Scientific Member and Director, Max Planck Institute for Mathematics, Bonn

Research Profile

The present foci of my work are spectral theory on one hand and the generalized Blaschke conjecture on the other. In spectral theory, my recent work deals with small eigenvalues of the Laplacian on complete Riemannian surfaces and an associated new invariant, the analytic systole. I also study the bottom of the spectrum of the Laplacian under Riemannian coverings, extending and generalizing previous work of Brooks. All this is joint work and project with three young mathematicians, Sugata Mondal, Henrik Matthiesen, and Panagiotis Polymerakis.
See https://arxiv.org/abs/1406.5836, https://arxiv.org/abs/1506.06541, and https://arxiv.org/abs/1611.00925

In the near future, I intend to concentrate more on the generalized Blasche conjecture. Say that a closed Riemannian manifold is a Blaschke manifold if its injectivity radius and diameter coincide. The generalized Blaschke conjecture then asserts that a Blaschke manifold is a compact rank one symmetric space (cross). Blaschke manifolds do have the cohomology of a cross and fall into corresponding types. Whereas the spherical type was solved by Berger, Kazdan, Weinstein, and Yang, the conjecture is open for the other types. This is a joint project with Karsten Grove. So far our main result is the uncovering of a serious mistake in one of the classical papers on the subject, pertaining to the diffeomorphism class of Blaschke manifolds of the complex projective type.
See also http://people.mpim-bonn.mpg.de/hwbllmnn/archiv/blaschke1603.pdf

Selected Publications

[1] Werner Ballmann, Henrik Matthiesen, Sugata Mondal
Small eigenvalues of closed surfaces
J. Differential Geom. , 103: (1): 1--13
2016
ISSN: 0022-040X
[2] Werner Ballmann, Jochen Brüning, Gilles Carron
Index theorems on manifolds with straight ends
Compos. Math. , 148: (6): 1897--1968
2012
ISSN: 0010-437X
DOI: 10.1112/S0010437X12000401
[3] Werner Ballmann, Jochen Brüning
On the spectral theory of manifolds with cusps
J. Math. Pures Appl. (9) , 80: (6): 593--625
2001
ISSN: 0021-7824
DOI: 10.1016/S0021-7824(00)01202-2
[4] W. Ballmann, J. Swiątkowski
On L2-cohomology and property (T) for automorphism groups of polyhedral cell complexes
Geom. Funct. Anal. , 7: (4): 615--645
1997
ISSN: 1016-443X
DOI: 10.1007/s000390050022
[5] Werner Ballmann, Michael Brin
Orbihedra of nonpositive curvature
Inst. Hautes Études Sci. Publ. Math. (82): 169--209 (1996)
1995
ISSN: 0073-8301
[6] W. Ballmann, M. Brin
Polygonal complexes and combinatorial group theory
Geom. Dedicata
, 50: (2): 165--191
1994
ISSN: 0046-5755
DOI: 10.1007/BF01265309
[7] Werner Ballmann, François Ledrappier
The Poisson boundary for rank one manifolds and their cocompact lattices
Forum Math. , 6: (3): 301--313
1994
ISSN: 0933-7741
DOI: 10.1515/form.1994.6.301

Publication List

Editorships

• International Journal of Mathematics (1989 - 1995)
• Geometriae Dedicata (1989 - 1999)
• Inventiones mathematicae (1996 - 2007)
• Mathematische Zeitschrift (1997 - 2003)
• Journal für die reine und angewandte Mathematik (Advisory Board, since 1990)
• Mathematical Proceedings, Cambridge Philosophical Society (since 2006)

Habilitations

Christian Bär (1993), now Professor, University of Potsdam

Bernhard Leeb (1997), now Professor, LMU Munich

Vicente Cortés (1999), now Professor, University of Hamburg

Dorothee Schueth (2000), now Professor, HU Berlin

Chand Devchand (2003), now Privatdozent, University of Potsdam

Alina Vdovina (2005), now Lecturer, Newcastle University, England, UK

Gregor Weingart (2005), now Researcher, National Autonomous University of Mexico, Mexico

Alexander Lytchak (2007), now Professor, University of Cologne

Thomas Vogel (2014), now Professor, LMU München

Selected PhD students

Paul Schmutz (1989): “Zur Anzahl kleiner Eigenwerte auf Riemannschen Flächen”

Christian Bär (1990): “Das Spektrum von Dirac-Operatoren”,
now Professor, University of Potsdam

Dorothee Schüth (1993): “Stetige isospektrale Deformationen”,
now Professor, HU Berlin

Vicente Cortés (1994): “Alekseevskiis quaternionische Kählermannigfaltigkeiten”,
now Professor, University of Hamburg

Gregor Weingart (1998): “Moduli Spaces of Minimal Isometric Immersions”,
now Researcher, National Autonomous University of Mexico, Mexico

Alexander Lytchak (2001): “Allgemeine Theorie der Submetrien und verwandte mathematische Probleme”,
now Professor, University of Cologne

Anna Wienhard (2004): “Bounded Cohomology and Geometry”,
now Professor, University of Heidelberg

Supervised Theses

  • Master theses: 10
  • Diplom theses: 45
  • PhD theses: 14, currently 3
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