Publications Werner Ballmann

  1. Random walks in hyperbolic spaces: Martin boundaries and bisectors
    (with P. Polymerakis).
    arxiv: 2408.13887
    Corrects and extends results of article 35.

  2. Equivariant discretizations of diffusions, random walks, and harmonic functions: corrections and additions
    (with P. Polymerakis). (pdf)
    L'Enseignement Math., accepted for publication.
    Corrects and extends results of articles 35 and 66.

  3. Spectral instability of coverings
    (with S. Mondal).
    Int. Math. Research Notices, accepted for publication.
    arxiv: 2311.14445

  4. Small eigenvalues of Schrödinger operators over geometrically finite manifolds
    (with P. Polymerakis).
    Math. Research Letters 31 (2024), no. 1, 1-24.
    Free access granted by International Press.

  5. On the essential spectrum of differential operators over geometrically finite orbifolds
    (with P. Polymerakis).
    J. Differential Geometry 127 (2024), no. 1, 1-34.

  6. On the differential form spectrum of geometrically finite orbifolds
    (with P. Polymerakis).
    arxiv: 2011.13304
    Main results superseded in article 70.

  7. On the spectrum of certain Hadamard manifolds
    (with M. Mukherjee and P. Polymerakis).
    SIGMA 19 (2023), 050, 19 pages.
    Open access

  8. Equivariant discretizations of diffusions and harmonic functions of bounded growth
    (with P. Polymerakis).
    Israel J. Math. 249 (2022), no. 1, 227-258.
    Open access funded by Max Planck Society.

  9. Equivariant discretizations of diffusions, random walks, and harmonic functions
    (with P. Polymerakis).
    L'Enseignement Math. 67 (2021), no. 3-4, 331-367.
    See article 73 for corrections and additions.

  10. Bottom of spectra and coverings of orbifolds
    (with P. Polymerakis).
    International J. Math. 32 (2021), no. 12, Paper No. 2140018, 33 pp.

  11. Bottom of spectra and coverings
    (with P. Polymerakis).
    Surveys in Differential Geometry 23 (2020), 1-33.

  12. Bottom of spectra and amenability of coverings
    (with H. Matthiesen and P. Polymerakis).
    Geometric Analysis, 17-35, Prog. Math. 333, Birkhäuser, 2020.
    Link to book

  13. Small eigenvalues of surfaces - old and new
    (with H. Matthiesen and S. Mondal).
    ICCM Notices 6 (2018), no. 2, 9-24.

  14. Introduction to Geometry and Topology. Translated by Walker Stern.
    Compact Textbooks in Mathematics. Birkhäuser, 2018. x+169 pp.
    Link to book

  15. Einführung in die Geometrie und Topologie. Zweite Auflage.
    Mathematik Kompakt. Birkhäuser, 2018. xii+163 pp.
    Link to book

  16. On the bottom of spectra under coverings
    (with H. Matthiesen and P. Polymerakis).
    Math. Zeitschrift 288 (2018), 1029-1036.
    Open access funded by Max Planck Society.

  17. On the analytic systole of Riemannian surfaces of finite type
    (with H. Matthiesen and S. Mondal).
    Geom. Funct. Analysis 27 (2017), 1070-1105.
    Open access funded by Max Planck Society.

  18. Small eigenvalues of surfaces of finite type
    (with H. Matthiesen and S. Mondal).
    Compositio Mathematica 153 (2017), 1747-1768.

  19. Guide to elliptic boundary value problems for Dirac-type operators
    (with C. Baer).
    Arbeitstagung Bonn 2013, 43-80, Prog. Math. 319, Birkhäuser, 2016.

  20. Small eigenvalues of closed surfaces
    (with H. Matthiesen and S. Mondal).
    J. Differential Geometry 103 (2016), 1-13.

  21. Einführung in die Geometrie und Topologie.
    Mathematik Kompakt. Birkhäuser, 2015. x+162 pp.

  22. On eta-functions for nilmanifolds.
    J. Differential Geometry 97 (2014), 1-10.

  23. Boundary value problems for elliptic differential operators of first order
    (with C. Baer).
    Surveys in Differential Geometry 17 (2012), 1-78.

  24. Index theorems on manifolds with straight ends
    (with J. Brüning and G. Carron).
    Compositio Mathematica 148 (2012), 1897-1968.
    arxiv: 1011.2290

  25. Periodic rank one geodesics in Hadamard spaces
    (with S. Buyalo).
    Contemporary Mathematics 469 (2008), 19-27.

  26. 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.

  27. Lectures on Kähler manifolds.
    ESI Lectures in Mathematics and Physics. EMS Publishing House, 2006. x+172 pp.
    Link to book

  28. On the construction of isospectral manifolds.
    Geometric Methods in Inverse Problems and PDE Control, 1-14, IMA Vol. Math. Appl. 137, Springer-Verlag, 2004.

  29. On the spectral theory of surfaces with cusps
    (with J. Brüning).
    Geometric Analysis and Nonlinear Partial Differential Equations, 13-37, Springer-Verlag, 2003.

  30. Eigenvalues and holonomy
    (with J. Brüning and G. Carron).
    International Math. Research Notices 12 (2003), 657-665.

  31. Spaces of nonpositive curvature.
    DMV-Jahrestagung 1999 in Mainz, Jahresbericht der Deutschen Mathematiker-Vereinigung 103 (2001), 52-65.

  32. On the spectral theory of manifolds with cusps
    (with J. Brüning).
    J. Math. Pures Appl. 80 (2001), 593-625.

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

  34. Rank rigidity of Euclidean polyhedra
    (with M. Brin).
    Amer. J. Math. 122 (2000), 873-885.

  35. On groups acting on nonpositively curved cubical complexes
    (with J. Swiatkowski).
    L'Enseignement Math. 45 (1999), 51-81.

  36. Diameter rigidity of spherical polyhedra
    (with M. Brin).
    Duke Math. J. 97 (1999), 235-259.

  37. Amenable isometry groups of Hadamard spaces
    (with S. Adams).
    Math. Annalen 312 (1998), 183-195.

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

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

  40. 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.
    See articles 73 and 74 for corrections and additions.

  41. Nonpositively curved metrics on 2-polyhedra
    (with S. Buyalo).
    Math. Zeitschrift 222 (1996), 97-134.

  42. Orbihedra of nonpositive curvature
    (with M. Brin).
    Publ. Math. IHES 82 (1995), 169-209.

  43. Lectures on spaces of nonpositive curvature. With an appendix by Misha Brin.
    DMV Seminar, 25. Birkhäuser, 1995. viii+112 pp.

  44. Polygonal complexes and combinatorial group theory
    (with M. Brin).
    Geometriae Dedicata 50 (1994), 165-191.

  45. The Poisson boundary for rank one manifolds and their cocompact lattices
    (with F. Ledrappier).
    Forum Math. 6 (1994), 301-313.

  46. Singular spaces of nonpositive curvature.
    Sur les groupes hyperboliques d'après Mikhael Gromov (Bern, 1988), 189-201, Prog. Math. 83, Birkhäuser, 1990.

  47. Manifolds of nonpositive curvature.
    DMV-Jahrestagung 1988 in Regensburg, Jahresbericht der Deutschen Mathematiker-Vereinigung 92 (1990), 145-152.

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

  49. On the Dirichlet problem at infinity for manifolds of nonpositive curvature.
    Forum Math. 1 (1989), 201-213.

  50. On the Dirichlet problem at infinity for manifolds of nonpositive curvature.
    Séminaire de théorie spectrale et géométrie Chambéry-Grenoble 7 (1988-89), 33-34.

  51. 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.

  52. On the differentiability of horocycles and horocycle foliations
    (with M. Brin and K. Burns).
    J. Differential Geometry 26 (1987), 337-347.

  53. On surfaces with no conjugate points
    (with M. Brin and K. Burns).
    J. Differential Geometry 25 (1987), 249-273.

  54. Fundamental groups of manifolds of nonpositive curvature
    (with P. Eberlein).
    J. Differential Geometry 25 (1987), 1-22.

  55. Structure of manifolds of nonpositive sectional curvature.
    Curvature and topology of Riemannian manifolds, 1-13, Lecture Notes in Math. 1201, Springer-Verlag, 1986.

  56. Geschlossene Geodätische auf Mannigfaltigkeiten mit unendlicher Fundamentalgruppe.
    Topology 25 (1986), 55-69.

  57. Manifolds of higher rank.
    W. Ballmann, M. Gromov, and V. Schroeder, Manifolds of nonpositive curvature, 177-192, Prog. Math. 61, Birkhäuser, 1985.

  58. Nonpositively curved manifolds of higher rank.
    Annals of Math. 122 (1985), 597-609.

  59. Structure of manifolds of nonpositive curvature. II
    (with M. Brin and R. Spatzier).
    Annals of Math. 122 (1985), 205-235.

  60. Structure of manifolds of nonpositive curvature. I
    (with M. Brin and P. Eberlein).
    Annals of Math. 122 (1985), 171-203.

  61. Manifolds of nonpositive curvature.
    Arbeitstagung Bonn 1984, pp. 261-268, Lecture Notes in Math. 1111, Springer-Verlag, 1985.

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

  63. 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.

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

  65. Existence of closed geodesics on positively curved manifolds
    (with G. Thorbergsson and W. Ziller).
    J. Differential Geometry 18 (1983), 221-252.

  66. On the lengths of closed geodesics on convex surfaces.
    Inventiones Math. 71 (1983), 593-597.

  67. On the ergodicity of geodesic flows
    (with M. Brin).
    Ergodic Theory Dynamical Systems 2 (1982), 311-315.

  68. On the number of closed geodesics on a compact Riemannian manifold
    (with W. Ziller).
    Duke Math. J. 49 (1982), 629-632.

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

  70. Axial isometries of manifolds of nonpositive curvature.
    Math. Annalen 259 (1982), 131-144.

  71. Closed geodesics and the fundamental group
    (with G. Thorbergsson and W. Ziller).
    Duke Math. J. 48 (1981), 585-588.

  72. Doppelpunktfreie geschlossene Geodätische auf kompakten Flächen.
    Math. Zeitschrift 161 (1978), 41-46.

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

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

Back to home page of Werner Ballmann