Publications Werner Ballmann

  1. Equivariant discretizations of diffusions, random walks, and harmonic functions
    (with P. Polymerakis).
    MPI-Preprint.
    arxiv.org/abs/1906.11716

  2. Bottom of spectra and amenability of coverings
    (with H. Matthiesen and P. Polymerakis).
    Geometric Analysis, Prog. Math., Birkhäuser, to appear.
    arxiv.org/abs/1803.07353

  3. Small eigenvalues of surfaces - old and new
    (with H. Matthiesen and S. Mondal).
    ICCM Notices 6 (2018), no. 2, 9-24.
    arxiv.org/abs/1710.00021
    doi 10.4310/ICCM.2018.v6.n2.a3

  4. Introduction to Geometry and Topology. Translated by Walker Stern.
    Compact Textbooks in Mathematics. Birkhäuser, 2018. x+169 pp.
    doi 10.1007/978-3-0348-0983-2 (Link)

  5. Einführung in die Geometrie und Topologie. Zweite Auflage.
    Mathematik Kompakt. Birkhäuser, 2018. xii+163 pp.
    doi 10.1007/978-3-0348-0986-3 (Link)

  6. On the bottom of spectra under coverings
    (with H. Matthiesen and P. Polymerakis).
    Math. Zeitschrift 288 (2018), 1029-1036.
    arxiv.org/abs/1701.02130
    doi 10.1007/s00209-017-1925-9
    Open access funding provided by Max Planck Society.

  7. On the analytic systole of Riemannian surfaces of finite type
    (with H. Matthiesen and S. Mondal).
    Geom. Funct. Analysis 27 (2017), 1070-1105.
    arxiv.org/abs/1611.00925
    doi 10.1007/s00039-017-0422-y
    Open access funding provided by Max Planck Society.

  8. Small eigenvalues of surfaces of finite type
    (with H. Matthiesen and S. Mondal).
    Compositio Mathematica 153 (2017), 1747-1768.
    arxiv.org/abs/1506.06541
    doi 10.1112/S0010437X17007291

  9. Guide to elliptic boundary value problems for Dirac-type operators
    (with C. Bär).
    Arbeitstagung Bonn 2013, 43-80, Prog. Math. 319, Birkhäuser, 2016.
    arxiv.org/abs/1307.3021
    doi 10.1007/978-3-319-43648-7_3

  10. Small eigenvalues of closed surfaces
    (with H. Matthiesen and S. Mondal).
    J. Differential Geometry 103 (2016), 1-13.
    arxiv.org/abs/1406.5836
    projecteuclid.org/euclid.jdg/1460463561

  11. Einführung in die Geometrie und Topologie.
    Mathematik Kompakt. Birkhäuser, 2015. x+162 pp.
    doi 10.1007/978-3-0348-0901-6

  12. On eta-functions for nilmanifolds.
    J. Differential Geometry 97 (2014), 1-10.
    projecteuclid.org/euclid.jdg/1404912100

  13. Boundary value problems for elliptic differential operators of first order
    (with C. Bär).
    Surveys in Differential Geometry 17 (2012), 1-78.
    arxiv.org/abs/1101.1196
    doi 10.4310/SDG.2012.v17.n1.a1

  14. Index theorems on manifolds with straight ends
    (with J. Brüning and G. Carron).
    Compositio Mathematica 148 (2012), 1897-1968.
    arxiv.org/abs/1011.2290
    doi 10.1112/S0010437X12000401

  15. Periodic rank one geodesics in Hadamard spaces
    (with S. Buyalo).
    Contemporary Mathematics 469 (2008), 19-27.
    doi 10.1090/conm/469/09159

  16. Regularity and index theory for Dirac-Schrödinger systems with Lipschitz coefficients
    (with J. Brüning and G. Carron).
    J. Math. Pures Appl. 89 (2008), 429-476.
    arxiv.org/abs/math/0703185
    doi 10.1016/j.matpur.2008.02.004

  17. Lectures on Kähler manifolds.
    ESI Lectures in Mathematics and Physics. EMS Publishing House, 2006. x+172 pp.
    doi 10.4171/025 (Link)

  18. On the construction of isospectral manifolds.
    Geometric Methods in Inverse Problems and PDE Control, 1-14, IMA Vol. Math. Appl. 137, Springer-Verlag, 2004.
    doi 10.1007/978-1-4684-9375-7_1

  19. On the spectral theory of surfaces with cusps
    (with J. Brüning).
    Geometric Analysis and Nonlinear Partial Differential Equations, 13-37, Springer-Verlag, 2003.
    doi 10.1007/978-3-642-55627-2_2

  20. Eigenvalues and holonomy
    (with J. Brüning and G. Carron).
    International Math. Research Notices 12 (2003), 657-665.
    arxiv.org/abs/math/0207045
    doi 10.1155/S1073792803207042

  21. Spaces of nonpositive curvature.
    DMV-Jahrestagung 1999 in Mainz, Jahresbericht der Deutschen Mathematiker-Vereinigung 103 (2001), 52-65.
    www.math.uni-bielefeld.de/jb_dmv/JB_DMV_103_2.pdf

  22. On the spectral theory of manifolds with cusps
    (with J. Brüning).
    J. Math. Pures Appl. 80 (2001), 593-625.
    doi 10.1016/S0021-7824(00)01202-2

  23. The Martin boundary of certain Hadamard manifolds. (pdf)
    Proceedings on Analysis and Geometry, 36-46, Sobolev Institute Press, Novosibirsk, 2000.

  24. Rank rigidity of Euclidean polyhedra
    (with M. Brin).
    Amer. J. Math. 122 (2000), 873-885.
    doi 10.1353/ajm.2000.0033

  25. On groups acting on nonpositively curved cubical complexes
    (with J. Swiatkowski).
    L'Enseignement Math. 45 (1999), 51-81.
    e-periodica.ch/digbib/volumes?UID=ens-001

  26. Diameter rigidity of spherical polyhedra
    (with M. Brin).
    Duke Math. J. 97 (1999), 235-259.
    doi 10.1215/S0012-7094-99-09711-9

  27. Amenable isometry groups of Hadamard spaces
    (with S. Adams).
    Math. Annalen 312 (1998), 183-195.
    doi 10.1007/s002080050218

  28. On L²-cohomology and property (T) for automorphism groups of polyhedral cell complexes
    (with J. Swiatkowski).
    Geom. Funct. Analysis 7 (1997), 615-645.
    doi 10.1007/s000390050022

  29. A volume estimate for piecewise smooth metrics on simplicial complexes.
    Rendiconti Sem. Mat. Fis. Milano 66 (1996), 323-331.
    doi 10.1007/BF02925363

  30. Discretization of positive harmonic functions on Riemannian manifolds and Martin boundary
    (with F. Ledrappier). (pdf)
    Actes de la table ronde de géométrie différentielle, 77-92, Semin. Congrés, Collection SMF 1, 1996.

  31. Nonpositively curved metrics on 2-polyhedra
    (with S. Buyalo).
    Math. Zeitschrift 222 (1996), 97-134.
    doi 10.1007/BF02621860

  32. Orbihedra of nonpositive curvature
    (with M. Brin).
    Publ. Math. IHES 82 (1995), 169-209.
    numdam.org/item?id=PMIHES_1995__82__169_0

  33. Lectures on spaces of nonpositive curvature. With an appendix by Misha Brin.
    DMV Seminar, 25. Birkhäuser, 1995. viii+112 pp.
    doi 10.1007/978-3-0348-9240-7

  34. Polygonal complexes and combinatorial group theory
    (with M. Brin).
    Geometriae Dedicata 50 (1994), 165-191.
    doi 10.1007/BF01265309

  35. The Poisson boundary for rank one manifolds and their cocompact lattices
    (with F. Ledrappier).
    Forum Math. 6 (1994), 301-313.
    doi 10.1515/form.1994.6.301

  36. Singular spaces of nonpositive curvature.
    Sur les groupes hyperboliques d'après Mikhael Gromov (Bern, 1988), 189-201, Prog. Math. 83, Birkhäuser, 1990.
    doi 10.1007/978-1-4684-9167-8_10

  37. Manifolds of nonpositive curvature.
    DMV-Jahrestagung 1988 in Regensburg, Jahresbericht der Deutschen Mathematiker-Vereinigung 92 (1990), 145-152.
    www.math.uni-bielefeld.de/JB_DMV/JB_DMV_092_4.pdf

  38. An estimate for the measure-theoretic entropy of geodesic flows
    (with M. Wojtkowski).
    Ergodic Theory Dynamical Systems 9 (1989), 271-279.
    doi 10.1017/S014338570000496X

  39. On the Dirichlet problem at infinity for manifolds of nonpositive curvature.
    Forum Math. 1 (1989), 201-213.
    doi 10.1515/form.1989.1.201

  40. On the Dirichlet problem at infinity for manifolds of nonpositive curvature.
    Séminaire de théorie spectrale et géométrie Chambéry-Grenoble 7 (1988-89), 33-34.
    numdam.org/item?id=TSG_1988-1989__7__33_0

  41. Manifolds of nonpositive sectional curvature and manifolds without conjugate points.
    Proceedings ICM, Vol. 1, 2 (Berkeley, Calif., 1986), 484-490, Amer. Math. Soc., Providence, RI, 1987.
    mathunion.org/ICM/ICM1986.1

  42. On the differentiability of horocycles and horocycle foliations
    (with M. Brin and K. Burns).
    J. Differential Geometry 26 (1987), 337-347.
    projecteuclid.org/euclid.jdg/1214441374

  43. On surfaces with no conjugate points
    (with M. Brin and K. Burns).
    J. Differential Geometry 25 (1987), 249-273.
    projecteuclid.org/euclid.jdg/1214440852

  44. Fundamental groups of manifolds of nonpositive curvature
    (with P. Eberlein).
    J. Differential Geometry 25 (1987), 1-22.
    projecteuclid.org/euclid.jdg/1214440722

  45. Structure of manifolds of nonpositive sectional curvature.
    Curvature and topology of Riemannian manifolds, 1-13, Lecture Notes in Math. 1201, Springer-Verlag, 1986.
    doi 10.1007/BFb0075644

  46. Geschlossene Geodätische auf Mannigfaltigkeiten mit unendlicher Fundamentalgruppe.
    Topology 25 (1986), 55-69.
    doi 10.1016/0040-9383(86)90005-4

  47. Manifolds of higher rank.
    W. Ballmann, M. Gromov, and V. Schroeder, Manifolds of nonpositive curvature, 177-192, Prog. Math. 61, Birkhäuser, 1985.
    doi 10.1007/978-1-4684-9159-3

  48. Nonpositively curved manifolds of higher rank.
    Annals of Math. 122 (1985), 597-609.
    doi 10.2307/1971331

  49. Structure of manifolds of nonpositive curvature. II
    (with M. Brin and R. Spatzier).
    Annals of Math. 122 (1985), 205-235.
    doi 10.2307/1971303

  50. Structure of manifolds of nonpositive curvature. I
    (with M. Brin and P. Eberlein).
    Annals of Math. 122 (1985), 171-203.
    doi 10.2307/1971373

  51. Manifolds of nonpositive curvature.
    Arbeitstagung Bonn 1984, pp. 261-268, Lecture Notes in Math. 1111, Springer-Verlag, 1985.
    doi 10.1007/BFb0084594

  52. Über geschlossene Geodätische. (pdf)
    Habilitationsschrift, Universität Bonn, Bonn, 1983, 66 pp.

  53. On the existence of short closed geodesics and their stability properties
    (with G. Thorbergsson and W. Ziller).
    Seminar on minimal submanifolds, 53-63, Annals of Math. Stud. 103, Princeton Univ. Press, 1983.

  54. Some existence theorems for closed geodesics
    (with G. Thorbergsson and W. Ziller).
    Comment. Math. Helv. 58 (1983), 416-432.
    doi 10.1007/BF02564645

  55. Existence of closed geodesics on positively curved manifolds
    (with G. Thorbergsson and W. Ziller).
    J. Differential Geometry 18 (1983), 221-252.
    projecteuclid.org/euclid.jdg/1214437662

  56. On the lengths of closed geodesics on convex surfaces.
    Inventiones Math. 71 (1983), 593-597.
    doi 10.1007/BF02095995

  57. On the ergodicity of geodesic flows
    (with M. Brin).
    Ergodic Theory Dynamical Systems 2 (1982), 311-315.
    doi 10.1017/S0143385700001632

  58. On the number of closed geodesics on a compact Riemannian manifold
    (with W. Ziller).
    Duke Math. J. 49 (1982), 629-632.
    doi 10.1215/S0012-7094-82-04932-8

  59. Closed geodesics on positively curved manifolds
    (with G. Thorbergsson and W. Ziller).
    Annals of Math. 116 (1982), 213-247.
    doi 10.2307/2007062

  60. Axial isometries of manifolds of nonpositive curvature.
    Math. Annalen 259 (1982), 131-144.
    doi 10.1007/BF01456836

  61. Closed geodesics and the fundamental group
    (with G. Thorbergsson and W. Ziller).
    Duke Math. J. 48 (1981), 585-588.
    doi 10.1215/S0012-7094-81-04832-8

  62. Doppelpunktfreie geschlossene Geodätische auf kompakten Flächen.
    Math. Zeitschrift 161 (1978), 41-46.
    doi 10.1007/BF01175611

  63. Einige neue Resultate über Mannigfaltigkeiten nichtpositiver Krümmung. (pdf)
    Dissertation, Bonner Math. Schriften 113, Universität Bonn, 1978. iv+57 pp.

  64. Der Satz von Lusternik und Schnirelmann. (pdf)
    Beiträge zur Differentialgeometrie, Heft 1, 1-25, Bonner Math. Schriften 102, Universität Bonn, 1978.


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