Prof. Dr. Gerhard Knieper

 

Adresse:
Ruhr-Uni­ver­si­tät Bo­chum
Fakultät für Mathematik
Lehrstuhl X (Analysis), Fach 42
Gebäude IB, Etage 3, Raum 183
Uni­ver­si­täts­stra­ße 150
D-44780 Bo­chum

Raum:
IB 3/183

Te­le­fon:
+49-(0)234/32-22381

E-Mail:
gerhard.knieper(at)rub.de

Publikationen

  • Egidi, Michela and Gerhard Knieper. “A quantitative closing Lemma and Partner orbits on Riemannian manifolds with negative curvature.” (2024) arXiv:2403.02077 
  • Knieper and B. Schulz, ‘Geodesic Anosov flows, hyperbolic closed geodesics and stable ergodicity’, Proceedings of the American Mathematical Society, vol. 2023, Feb. 2023, doi: 10.1090/proc/16423.
  • G. Contreras, G. Knieper, M. Mazzucchelli, and B. Schulz, ‘Surfaces of section for geodesic flows of closed surfaces’, 2022, https://doi.org/10.48550/arXiv.2204.11977
  • V. Climenhaga, G. Knieper, and K. War, ‘Closed geodesics on surfaces without conjugate points’, Communications in contemporary mathematics, vol. 24, no. 6, Art. no. 2150067, 2022, doi: 10.1142/s021919972150067x.
  • C. Guillarmou, G. Knieper, and T. Lefeuvre, ‘Geodesic stretch, pressure metric and marked length spectrum rigidity’, Ergodic theory and dynamical systems, vol. 42, no. 3, pp. 974–1022, 2022, doi: 10.1017/etds.2021.75.
  • V. Climenhaga, G. Knieper, and K. War, ‘Uniqueness of the measure of maximal entropy for geodesic flows on certain manifolds without conjugate points’, Advances in mathematics, vol. 376, Art. no. 107452, Oct. 2020, doi: 10.1016/j.aim.2020.107452.
  • G. Knieper, J. R. Parker, and N. Peyerimhoff, ‘Minimal codimension one foliation of a symmetric space by Damek-Ricci spaces’, Differential geometry and its applications, vol. 69, Art. no. 101605, Feb. 2020, doi: 10.1016/j.difgeo.2020.101605.
  • K. Biswas, G. Knieper, and N. Peyerimhoff, ‘The Fourier transform on harmonic manifolds of purely exponential volume growth’, The journal of geometric analysis, vol. 31, no. 1, pp. 126–163, Aug. 2019, doi: 10.1007/s12220-019-00253-9.
  • G. Knieper, ‘A note on Anosov flows of non-compact Riemannian manifolds’, Proceedings of the American Mathematical Society, vol. 146, no. 9, pp. 3955–3959, 2018, doi: 10.1090/proc/14096.
  • G. Knieper, ‘A survey on noncompact harmonic and asymptotically harmonic manifolds’, in Geometry, topology, and dynamics in negative curvature, Bangalore, 2016, vol. 425, pp. 146–197. doi: 10.1017/cbo9781316275849.006.
  • G. Knieper and N. Peyerimhoff, ‘Geometric properties of rank one asymptotically harmonic manifolds’, Journal of differential geometry, vol. 100, no. 3, pp. 507–532, 2015, doi: 10.4310/jdg/1432842363.
  • G. Knieper and N. Peyerimhoff, ‘Harmonic functions on rank one asymptotically harmonic manifolds’, The journal of geometric analysis, vol. 26, no. 2, pp. 750–781, 2015, doi: 10.1007/s12220-015-9570-1.
  • E. Glasmachers, G. Knieper, C. Ogouyandjou, and J. P. Schröder, ‘Topological entropy of minimal geodesics and volume growth on surfaces’, Journal of modern dynamics, vol. 8, no. 1, pp. 75–91, 2014, doi: 10.3934/jmd.2014.8.75.
  • G. Knieper, ‘New results on noncompact harmonic manifolds’, Commentarii mathematici Helvetici, vol. 87, no. 3, pp. 669–703, 2012, doi: 10.4171/cmh/265. http://arxiv.org/abs/0910.3872
  • E. Glasmachers and G. Knieper, ‘Minimal geodesic foliation on T^2 in case of vanishing topological entropy’, Journal of topology and analysis, vol. 3, no. 4, pp. 511–520, 2011, doi: 10.1142/s1793525311000623.
  • G. Knieper and E. Glasmachers, ‘Characterization of geodesic flows on T2 with and without positive topological entropy’, Geometric and functional analysis, vol. 20, no. 5, pp. 1259–1277, 2010, doi: 10.1007/s00039-010-0087-2.
  • A. Altland, P. Braun, F. Haake, S. Heusler, G. Knieper, and S. Müller, ‘Near action-degenerate periodic-orbit bunches: a skeleton of chaos’, in Path integrals, 2008, pp. 40–47. doi: 10.1142/9789812837271_0005.
  • G. Knieper and N. Peyerimhoff, ‘Ergodic properties of isoperimetric domains in spheres’, Journal of modern dynamics, vol. 2, no. 2, pp. 339–358, 2008, doi: 10.3934/jmd.2008.2.339.
  • J. O. Heber, G. Knieper, and H. M. Shah, ‘Asymptotically harmonic spaces in dimension 3’, Proceedings of the American Mathematical Society, vol. 135, no. 3, pp. 845–849, 2007, doi: 10.1090/s0002-9939-06-08520-0.
  • G. Knieper, ‘The uniqueness of the maximal measure for geodesic flows on symmetric spaces of higher rank’, Israel journal of mathematics, vol. 149, pp. 171–183, 2005, doi: 10.1007/bf02772539.
  • M. Coornaert and G. Knieper, ‘An upper bound for the growth of conjugacy classes in torsion-free word hyperbolic groups’, International journal of algebra and computation, vol. 14, no. 4, pp. 395–401, 2004, doi: 10.1142/s0218196704001803.
  • M. Coornaert and G. Knieper, ‘Growth of conjugacy classes in Gromov hyperbolic groups’, Geometric and functional analysis, vol. 12, no. 3, pp. 464–478, 2002, doi: 10.1007/s00039-002-8254-8.
  • G. Knieper, ‘Hyperbolic dynamics and Riemannian geometry’, in Handbook of dynamical systems, 1. ed., B. Hasselblatt and A. Katok, Eds. Amsterdam: Elsevier, 2002, pp. 453–545. doi: 10.1016/s1874-575x(02)80008-x.
  • G. Knieper and H. Weiss, ‘C∞ Genericity of Positive Topological Entropy for Geodesic Flows on S2’, Journal of differential geometry, vol. 62, no. 1, pp. 127–141, 2002, doi: 10.4310/jdg/1090425531.
  • G. Knieper, ‘Closed geodesics and the uniqueness of the maximal measure for rank 1 geodesic flows’, in Smooth ergodic theory and its applications, 2001, vol. 69, pp. 573–590.
  • G. Knieper, ‘The uniqueness of the measure of maximal entropy for geodesic flows on rank 1 manifolds’, Annals of mathematics / Institute for Advanced Study, vol. 148, no. 1, pp. 291–314, 1998, doi: 10.2307/120995.
  • G. Knieper, ‘On the asymptotic geometry of nonpositively curved manifolds’, Geometric and functional analysis, vol. 7, no. 4, pp. 755–782, 1997, doi: 10.1007/s000390050025.
  • G. Knieper, ‘A second derivative formula of the Liouville entropy at spaces of constant negative curvature’, Ergodic theory and dynamical systems, vol. 17, no. 5, pp. 1131–1135, 1997, doi: 10.1017/s0143385797086446.
  • G. Knieper, ‘Volume growth, entropy and the geodesic stretch’, Mathematical research letters, vol. 2, no. 1, pp. 39–58, 1995, [Online].
  • G. Knieper, ‘Spherical means on compact Riemannian manifolds of negative curvature’, Differential geometry and its applications, vol. 4, no. 4, pp. 361–390, 1994, doi: 10.1016/0926-2245(94)90004-3.
  • G. Knieper and H. Weiss, ‘A surface with positive curvature and positive topological entropy’, Journal of differential geometry, vol. 39, no. 2, pp. 229–249, 1994, doi: 10.4310/jdg/1214454871.
  • G. Knieper, ‘Der geodätische Fluss einer Riemannschen Mannigfaltigkeit und die Entropie’, in Geometrie und Physik, vol. 8, W. Müller, Ed. Berlin: De Gruyter, 1993, pp. 15–24.
  • A. Katok, G. Knieper, and H. Weiss, ‘Formulas for the derivative and critical points of topological entropy for Anosov and geodesic flows’, Communications in mathematical physics, vol. 138, no. 1, pp. 19–31, 1991, doi: 10.1007/bf02099667.
  • K. Burns and G. Knieper, ‘Rigidity of surfaces with no conjugate points’, Journal of differential geometry, vol. 34, no. 3, pp. 623–650, 1991, doi: 10.4310/jdg/1214447537.
  • A. Katok, G. Knieper, M. Pollicott, and H. Weiss, ‘Differentiability of entropy for Anosov and geodesic flows’, Bulletin of the American Mathematical Society, vol. 22, no. 2, pp. 285–293, 1990, doi: 10.1090/s0273-0979-1990-15889-6.
  • G. Knieper and H. Weiss, ‘Regularity of entropy for geodesic flows’, in Recent developments in geometry, 1989, vol. 101, pp. 191–196.
  • G. Knieper and H. Weiss, ‘Regularity of measure theoretic entropy for geodesic flows of negative curvature: I’, Inventiones mathematicae, vol. 95, no. 3, pp. 579–589, 1989, doi: 10.1007/bf01393891.
  • A. Katok, G. Knieper, M. Pollicott, and H. Weiss, ‘Differentiability and analyticity of topological entropy for Anosov and geodesic flows’, Inventiones mathematicae, vol. 98, no. 3, pp. 581–597, 1989, doi: 10.1007/bf01393838.
  • G. Knieper, Mannigfaltigkeiten ohne konjugierte Punkte. Bonn: Math. Inst. d. Univ., Bibliothek, 1986.
  • G. Knieper, ‘Das Wachstum der Äquivalenzklassen geschlossener Geodätischer in kompakten Mannigfaltigkeiten’, Archiv der Mathematik, vol. 40, no. 6, pp. 559–568, 1983.

Skript Kurven und Flächen

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