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Durham University

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Staff Profile

Norbert Peyerimhoff, PhD University of Augsburg

Personal web page

Professor, Geometry in the Department of Mathematical Sciences
Telephone: +44 (0) 191 33 43114
Room number: CM320

(email at

Research Groups

Department of Mathematical Sciences

  • Pure Mathematics
  • Pure Mathematics: Geometry

Research Interests

  • Global Analysis
  • Graph Theory
  • Riemannian Geometry

Selected Publications

Chapter in book

  • Cushing, David, Liu, Shiping, Muench, Florentin & Peyerimhoff, Norbert (2020). Curvature Calculations for Antitrees. In Analysis and Geometry on Graphs and Manifolds. Keller, Matthias, Lenz, Daniel & Wojciechowski, Radoslaw K. Cambridge: Cambridge University Press. 461: 21-54.
  • Liu, Shiping, Peyerimhoff, Norbert & Vdovina, Alina (2020). Signatures, Lifts, and Eigenvalues of Graphs. In Discrete and Continuous Models in the Theory of Networks. Atay, Fatihcan M., Kurasov, Pavel B. & Mugnolo, Delio Birkhäuser. 281: 255-269.

Journal Article

  • Kleemiss, Florian, Dolomanov, Oleg V., Bodensteiner, Michael, Peyerimhoff, Norbert, Midgley, Laura, Bourhis, Luc J., Genoni, Alessandro, Malaspina, Lorraine A., Jayatilaka, Dylan, Spencer, John L, White, Fraser, Grundkötter-Stock, Bernhard, Steinhauer, Simon, Lentz, Dieter, Puschmann, Horst & Grabowsky, Simon (2021). Accurate Crystal Structures and Chemical Properties from NoSpherA2. Chemical Science
  • Biswas, Kingshook Knieper, Gerhard & Peyerimhoff, Norbert (2021). The Fourier Transform on harmonic manifolds of purely exponential volume growth. The Journal of Geometric Analysis 31(1): 126-163.
  • Keller, Matthias, Liu, Shiping & Peyerimhoff, Norbert (2020). A note on eigenvalue bounds for non-compact manifolds. Mathematische Nachrichten
  • Peyerimhoff, Norbert & Samiou, Evangelia (2020). A support theorem for the X-ray transform on manifolds with plane covers. Mathematical Proceedings of the Cambridge Philosophical Society 169(1): 149-158.
  • Cushing, David, Liu, Shiping & Peyerimhoff, Norbert (2020). Bakry-Émery Curvature Functions on Graphs. Canadian Journal of Mathematics 72(1): 89-143.
  • Cushing, David, Kamtue, Supanat, Kangaslampi, Riikka, Liu, Shiping & Peyerimhoff, Norbert (2020). Curvatures, Graph Products and Ricci Flatness. Journal of Graph Theory
  • Peyerimhoff, Norbert & Taeufer, Matthias (2020). Eigenfunctions and the Integrated Density of States on Archimedean Tilings. Journal of Spectral Theory
  • Cushing, David, Kamtue, Supanat, Peyerimhoff, Norbert & Watson May, Leyna (2020). Quartic graphs which are Bakry-Émery curvature sharp. Discrete Mathematics 343(3): 111767.
  • Cushing, David, Kamtue, Supanat, Liu, Shiping, Muench, Florentin & Peyerimhoff, Norbert (2020). Rigidity of the Bonnet-Myers inequality for graphs with respect to Ollivier Ricci curvature. Advances in Mathematics 369: 107188.
  • Liu, Shiping, Muench, Florentin & Peyerimhoff, Norbert (2019). Curvature and higher order Buser inequalities for the graph connection Laplacian. SIAM Journal on Discrete Mathematics (SIDMA) 33(1): 257-305.
  • Liu, Shiping, Münch, Florentin, Peyerimhoff, Norbert & Rose, Christian (2019). Distance Bounds for Graphs with Some Negative Bakry-Émery Curvature. Analysis and Geometry in Metric Spaces 7(1): 1-14.
  • Egidi, Michela Liu, Shiping , Muench, Florentin & Peyerimhoff, Norbert (2019). Ricci curvature and eigenvalue estimates for the magnetic Laplacian on manifolds. Communication in Analysis and Geometry
  • Ivrissimtzis, Ioannis, Peyerimhoff, Norbert & Vdovina, Alina (2019). Trivalent expanders, $(Delta – Y)$-transformation, and hyperbolic surfaces. Groups, Geometry, and Dynamics 13(3): 1103-1131.
  • Liu, Shiping, Münch, Florentin & Peyerimhoff, Norbert (2018). Bakry–Émery curvature and diameter bounds on graphs. Calculus of Variations and Partial Differential Equations 57(2): 67.
  • Liu, Shiping & Peyerimhoff, Norbert (2018). Eigenvalue ratios of non-negatively curved graphs. Combinatorics, probability and computing 27(5): 829-850.
  • Parker, John R, Peyerimhoff, Norbert & Siburg, Karl Friedrich (2018). Minimizing length of billiard trajectories in hyperbolic polygons. Conformal Geometry and Dynamics 22: 315-332.
  • Bourne, D.P., Cushing, D., Liu, S., Muench, F. & Peyerimhoff, N. (2018). Ollivier-Ricci idleness functions of graphs. SIAM Journal on Discrete Mathematics 32(2): 1408-1424.
  • Keller, Matthias, Peyerimhoff, Norbert & Pogorzelski, Felix (2017). Sectional curvature of polygonal complexes with planar substructures. Advances in Mathematics 307: 1070-1107.
  • Peyerimhoff, N., Täufer, M. & Veselić, I. (2017). Unique continuation principles and their absence for Schrödinger eigenfunctions on combinatorial and quantum graphs and in continuum space. Nanosystems: Physics, Chemistry, Mathematics 8(2): 216-230.
  • Knieper, Gerhard & Peyerimhoff, Norbert (2016). Harmonic Functions on Rank One Asymptotically Harmonic Manifolds. The Journal of Geometric Analysis 26(2): 750-781.
  • Barker, N., Boston, N., Peyerimhoff, N. & Vdovina, A. (2015). An infinite family of 2-groups with mixed Beauville structures. International Mathematics Research Notices 2015(11): 3598-3618.
  • Lange, Carsten, Liu, Shiping, Peyerimhoff, Norbert & Post, Olaf (2015). Frustration index and Cheeger inequalities for discrete and continuous magnetic Laplacians. Calculus of Variations and Partial Differential Equations 54(4): 4165-4196.
  • Knieper, G. & Peyerimhoff, N. (2015). Geometric properties of rank one asymptotically harmonic manifolds. Journal of Differential Geometry 100(3): 507-532.
  • Peyerimhoff, Norbert & Samiou, Evangelia (2015). Integral Geometric Properties of Non-compact Harmonic Spaces. The Journal of Geometric Analysis 25(1): 122.
  • Leonhardt, Karsten, Peyerimhoff, Norbert, Tautenhahn, Manfred & Veselic, Ivan (2015). Wegner estimate and localization for alloy-type models with sign-changing exponentially decaying single-site potentials. Reviews in Mathematical Physics 27(04): 1550007.
  • Castle, S., Peyerimhoff, N. & Siburg, K. F. (2011). Billiards in ideal hyperbolic polygons. Discrete and Continuous Dynamical Systems - Series A 29(3): 893-908.
  • Peyerimhoff, N & Vdovina, A (2011). Cayley graph expanders and groups of finite width. Journal of Pure and Applied Algebra 215(11): 2780-2788.
  • Keller, M & Peyerimhoff, N (2011). Cheeger constants, growth and spectrum of locally tessellating planar graphs. Mathematische Zeitschrift 268(3-4): 871-886.
  • Peyerimhoff, N. & Samiou, E. (2010). Spherical spectral synthesis and two-radius theorems on Damek-Ricci spaces. Arkiv för Matematik 48(1): 131-147.
  • Lenz, D., Peyerimhoff, N., Post, O. & Veselic, I. (2009). Continuity of the integrated density of states on random length metric graphs. Mathematical Physics, Analysis and Geometry 12(3): 219-254.
  • Lenz, D., Peyerimhoff, N., Post, O. & Veselic, I. (2008). Continuity properties of the integrated density of states on manifolds. Japanese Journal of Mathematics 3(1): 121-161.
  • Knieper, G. & Peyerimhoff, N. (2008). Ergodic properties of isoperimetric domains in spheres. Journal of Modern Dynamics 2(2): 339-358.
  • Baues, O. & Peyerimhoff, N. (2006). Geodesics in non-positively curved plane tessellations. Advances in Geometry 6(2): 243-263.
  • Peyerimhoff, N. (2006). Spherical means on compact locally symmetric spaces of non-positive curvature. Forum Mathematicum 18(3): 391-417.
  • Lenz, D., Peyerimhoff, N. & Veselic, I. (2004). Integrated density of states for random metrics on manifolds. Proceedings of the London Mathematical Society 88(3): 733-752.
  • Peyerimhoff, N. & Siburg, K. F. (2003). The dynamics of magnetic flows for energies above Mane's critical value. Israel Journal of Mathematics 135: 269-298.
  • Peyerimhoff, N. (2002). Simplices of maximal volume or minimal total edge length in hyperbolic space. Journal of the London Mathematical Society 66(3): 753-768.

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