Publications

  1. Small eigenvalues of surfaces - old and new.
    (with H. Matthiesen and S. Mondal).
    arxiv.org/abs/1710.00021

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

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

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

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

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

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

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

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

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

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

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

  13. Lectures on Kähler manifolds.
    ESI Lectures in Mathematics and Physics. EMS Publishing House, 2006. x+172 pp.
    doi.org/10.4171/025

  14. 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.org/10.1007/978-1-4684-9375-7_1

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

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

  17. Spaces of nonpositive curvature.
    Jahresberichte DMV 103 (2001), 52-65.
    www.math.uni-bielefeld.de/jb_dmv/JB_DMV_103_2.pdf

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

  33. Manifolds of nonpositive curvature.
    Jahresberichte DMV 92 (1990), 145-152.
    www.math.uni-bielefeld.de/JB_DMV/JB_DMV_092_4.pdf

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

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

  36. 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

  37. 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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

  60. 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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