Prof. Dr. Gerhard Knieper
Ruhr-Universität Bochum
Fakultät für Mathematik
Lehrstuhl X (Analysis), Fach 42
Gebäude IB, Etage 3, Raum 183
D-44780 Bochum
Telefon: +49-(0)234/32-22381
E-mail: gerhard.knieper@rub.de
Liste der Veröffentlichungen
- G. Contreras, G. Knieper, M. Mazzucchelli, B. Schulz, Surfaces of section for geodesic flows of closed surfaces , arXiv:2204.11977
- G. Knieper, B. Schulz, Geodesic Anosov flows, hyperbolic closed geodesics and stable ergodicity, arXiv:2202.05084.
- V. Climenhaga, G. Knieper, K. War, Closed geodesics on surfaces without conjugate points, Commun. Contemp. Math.,1-35.
- C. Guillarmou, G. Knieper, T. Lefeuvre, Geodesic stretch, pressure metric and marked length spectrum rigidity, Ergodic Theory Dynam. Systems, 42 (2022), 974--1022.
- K. Biswas, G. Knieper, N. Peyerimhoff, The Fourier Transform on Harmonic manifolds of purely exponential volume growth, J. Geom. Anal. 31 (2021), no. 1, 126–163.
- V. Climenhaga, G. Knieper, K. War, Uniqueness of the measure of maximal entropy for geodesic flows on certain manifolds without conjugate points, Adv. Math. 376 (2021), 107452, 44 pp.
- G. Knieper, J. R. Parker, N. Peyerimhoff, Minimal codimension one foliation of a symmetric space by Damek-Ricci spaces, Differential Geom. Appl. 69, (2020).
- G. Knieper, A note on Anosov flows of noncompact Riemannian manifolds, Proc. Amer. Math. Soc. 146 (2018), no. 9, 3955–3959. 37D40 (53C22).
- G. Knieper, A survey on noncompact harmonic and asymptotically harmonic manifolds, Geometry, topology, and dynamics in negative curvature, 146-197, London Math. Soc. Lecture Note Ser., 425, Cambridge Univ. Press, Cambridge, 2016.
- G. Knieper, N. Peyerimhoff, Harmonic functions on rank one asymptotically harmonic manifolds, J. Geom. Anal., 26, no. 2, (2016), 750-781.
- G. Knieper, N. Peyerimhoff, Geometric properties of rank one asymptotically harmonic manifolds, J. Differential Geom., 100, no. 3, (2015), 507-532.
- E. Glasmachers, G. Knieper, C. Ogouyandjou, J. P. Schröder, Topological entropy of minimal geodesics and volume growth on surfaces, J. Mod. Dyn., 8, no. 1, 2014, 75-91.
- G. Knieper, New results on noncompact harmonic manifolds, Comment. Math. Helv. 87, no. 3 (2012), 669-703.
- E. Glasmachers, G. Knieper, Minimal geodesic foliations geodesic flows on T² in case of vanishing topological entropy, J. Topol. Anal., 3, no. 4 (2011), 511-520.
- E. Glasmachers, G. Knieper, Characterization of geodesic flows on T² with and without positive topological entropy, Geom. Funct. Anal. 20, no. 5, (2010), 1259-1277.
- A. Altland, P. Braun, F. Haake, S. Heusler, G. Knieper, S. Müller, Near action-degenerate periodic-orbit bunches: a skeleton of chaos, Path integrals, 40-47, World Sci. Publ., Hackensack, NJ, 2008.
- G. Knieper, N. Peyerimhoff, Ergodic properties of isoparametric domains in spheres, J. Mod. Dyn. 2, no. 2 (2008), 1-20.
- J. Heber, G. Knieper, H. Shah, Asymptotically harmonic spaces in dimension 3, Proc. Amer. Math. Soc. 135, no. 3, (2007), 845-849.
- G. Knieper, The uniqueness of the maximal measure for geodesic flows on symmetric spaces of higher rank, Israel J. Math. 149 (2005), 171-183.
- M. Coornaert, G. Knieper, An upper bound for the growth of conjugacy classes in torsionfree word hyperbolic groups, Internat. J. Algebra Comput. 14, no. 4, (2004), 395-401.
- G. Knieper, H. Weiss, C∞ genericity of positive topological entropy for geodesic flows on S², J. Differential Geom. 62, no. 1, (2002), 127-141.
- M. Coornaert, G. Knieper, Growth of conjugacy classes in Gromov hyperbolic groups, Geom. Funct. Anal. 12, no. 3, (2002), 464-478.
- G. Knieper, Hyperbolic Dynamics and Riemannian Geometry, Handbook of Dynamical Systems, vol. 1A, 453-545, North-Holland, Amsterdam, 2002.
- G. Knieper, Closed geodesics and the uniqueness of the maximal measure for rank 1 geodesic flows, Smooth ergodic theory and its applications, (Seattle, WA, 1999), 573-590, Proc. Sympos. Pure Math. 69 Amer. Math. Soc., Providence, RI, 2001.
- G. Knieper, The uniqueness of the measure of maximal entropy for rank 1 manifolds, Annals of Math. (2) 148, no. 1, (1998), 291-314.
- G. Knieper, On the asymptotic geometry of nonpositively curved manifolds, Geom. Funct. Anal. 7, no. 4, (1997), 755-782.
- G. Knieper, A second derivative formula of the Liouville entropy at spaces of constant negative curvature, Ergodic Theory Dynam. Sys. 17, no. 5, (1997), 1131-1135.
- G. Knieper, Volume growth, entropy and the geodesic stretch, Math. Res. Lett. 2, no. 1, (1995), 1-20.
- G. Knieper, Spherical means on compact Riemannian manifolds of negative curvature, Differential Geom. Appl. 4, no. 4, (1994), 361-390.
- G. Knieper, H. Weiss, A surface with positive curvature and positive topological entropy, J. Differential Geom. 39, no. 2, (1994), 229-249.
- G. Knieper, Der geodätische Fluß einer Riemannschen Mannigfaltigkeit und die Entropie (The geodesic flow of a Riemannian manifold and entropy), 15-24, Geometrie und Physik, Forschungsbericht 8, Akademie der Wissenschaften zu Berlin, de Gruyter (1993).
- K. Burns, G. Knieper, Rigidity of surfaces with no conjugate points, J. Differential Geom. 34, no. 3, (1991), 623-650.
- A. Katok, G. Knieper, H. Weiss, Formulas for the derivative and critical points of topological entropy for Anosov and geodesic flows, Comm. Math. Phys. 138, no. 1, (1991), 19-31.
- A. Katok, G. Knieper, M. Pollicott, H. Weiss, Differentiability of entropy for Anosov and geodesic flows, Bull. Am. Math. Soc., New Ser. 22, no. 2 (1990), 285-293.
- A. Katok, G. Knieper, M. Pollicott, H. Weiss, Differentiability and analyticity of topological entropy for Anosov and geodesic flows, Invent. Math. 98, no.3 (1989), 581-597.
- G. Knieper, H. Weiss, Regularity of measure theoretic entropy for geodesic flows of negative curvature, Invent. Math. 95, no. 3, (1989), 579-589.
- G. Knieper, H. Weiss, Regularity of entropy for geodesic flows, Recent Developments in Geometry, (Los Angeles, CA, 1987), 191-196, Contemp. Math. 101, Am. Math. Soc., Providence, RI, 1989.
- G. Knieper, Mannigfaltigkeiten ohne konjugierte Punkte (Manifolds without conjugate points), Dissertation, Bonn. Math. Schr. 168 (1986).
- G. Knieper, Das Wachstum der Äquivalenzklassen geschlossener Geodätischer in kompakten Mannigfaltigkeiten (The growth rate of equivalence classes of closed geodesics in compact manifolds), Arch. Math. (Basel) 40, no. 6, (1983), 559-568.