Publications Werner Ballmann

  1. Small eigenvalues of Schrödinger operators over geometrically finite manifolds
    (with P. Polymerakis).
    MPIM Preprint 2021-30.

  2. On the essential spectrum of differential operators over geometrically finite orbifolds
    (with P. Polymerakis).
    MPIM Preprint 2021-9.

  3. On the differential form spectrum of geometrically finite orbifolds
    (with P. Polymerakis).
    MPIM Preprint 2020-62.
    Comment: This paper will not be submitted anymore for publication in a journal since its main results are superseded in arxiv:2103.13704.

  4. Bottom of spectra and coverings of orbifolds
    (with P. Polymerakis).
    International J. Math. 32 (2021), to appear.

  5. Equivariant discretizations of diffusions and harmonic functions of bounded growth
    (with P. Polymerakis).
    Israel J. Math., to appear.

  6. Equivariant discretizations of diffusions, random walks, and harmonic functions
    (with P. Polymerakis).
    L'Enseignement Math., to appear.

  7. Bottom of spectra and coverings
    (with P. Polymerakis).
    Surveys in Differential Geometry 23 (2020), 1-33.
    doi 10.4310/SDG.2018.v23.n1.a1

  8. Bottom of spectra and amenability of coverings
    (with H. Matthiesen and P. Polymerakis).
    Geometric Analysis, 17-35, Prog. Math. 333, Birkhäuser, 2020.
    doi 10.1007/978-3-030-34953-0_2 (Link)

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

  10. 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)

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

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

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

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

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

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

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

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

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

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

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

  22. 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.
    doi 10.1016/j.matpur.2008.02.004

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

  24. 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

  25. 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

  26. Eigenvalues and holonomy
    (with J. Brüning and G. Carron).
    International Math. Research Notices 12 (2003), 657-665.
    doi 10.1155/S1073792803207042

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

  28. 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

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

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

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

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

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

  34. 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

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

  36. 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.

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

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

  39. 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

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

  41. 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

  42. 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

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

  44. 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

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

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

  47. 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.

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

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

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

  51. 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

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

  53. 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

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

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

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

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

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

  59. 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.

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

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

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

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

  64. 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

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

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

  67. 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

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

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

  70. 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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