PD Dr. habil. Olaf Müller

Lehrkraft für besondere Aufgaben
Institut für Mathematik
Humboldt-Universität zu Berlin


E-mail: mullerol (then the usual symbol in between) math.hu-berlin.de
For Erasmus issues , please use erasmus.math@hu....
Tel.: +49 (0) 30 2093 45435
Office: RUD25-1.308
Office hour: (winter term 2024-2025): Fridays 11am to 12am, or by appointment


For information about current teaching

Please consult my German homepage

Teaser for my seminar about systolic inequalities and filling problems a la Gromov (Summer term 2022)


Research interests

  • Cauchy problems of quasi-linear hyperbolic equations
  • Geometry of of infinite-dimensional Frechet manifolds of sections and inverse-function theorems
  • Geometry at infinity (asymptotic geometry of noncompact manifolds, ideal boundaries)
  • Conformal geometry, Yamabe Theory
  • Geometry of globally hyperbolic manifolds,e.g. Special time functions
  • Spin geometry and Dirac operators
  • Geodesic dynamics and dynamics of minimal submanifolds
  • Entropy, synthetic curvature and Optimal Transport


Published articles

  1. Lorentzian Gromov-Hausdorff theory and finiteness results
    Gen Relativ Gravit 54, 117 (2022)
    arXiv:1912.00988

  2. Solutions to the Dirac Equation in Kerr-Newman Geometries including the black-hole region, with Christoph Krpoun.
    Accepted for publication by Journal of Geometry and Physics (2022)
    arXiv:2204.05741

  3. Construction of initial data sets for Lorentzian manifolds with lightlike parallel spinors, mit Bernd Ammann und Klaus Kroencke . Communications in Mathematical Physics 387, 77-109 (2021)
    arXiv:1903.02064

  4. On the von Neumann rule in quantization
    Journal of Mathematical Physics 60, 082104 (2019)
    arxiv:1903.10494

  5. Black holes in Einstein-Maxwell Theory,
    Class.Quant.Grav. 36, no 1 (2018)
    arxiv: 1607.05036

  6. Global solvability of massless Dirac–Maxwell systems, with Nicolas Ginoux
    Annales de l'Institut Henri Poincaré C, Analyse non linéaire 35, no 6, 1645-1654 (2018)
    arXiv:1407.1177 [math-ph]

  7. Applying the index theorem for non-smooth operators
    Journal of Geometry and Physics 116, 140-145 (2017)
    arXiv:1506.04636 [math-ph]

  8. A universal spinor bundle and the Einstein–Dirac–Maxwell equation as a variational theory, with Nikolai Nowaczyk
    Letters in Mathematical Physics 107, 933–961 (2017)
    arXiv:1504.01034 [math-ph]

  9. Riemannian geometry of the space of volume preserving immersions, with Martin Bauer and Peter Michor
    Differential Geometry and its Applications 49, 23-42 (2016)
    arXiv:1603.0591616

  10. Which spacetimes admit conformal compactifications?
    Advances in Theoretical and Mathematical Physics 20, no. 5, 1109-1124 (2016)
    arXiv:1409.8136 [math-ph]

  11. Lorentzian Spectral Geometry for Globally Hyperbolic Surfaces, with Felix Finster.
    Advances in Theoretical and Mathematical Physics 20,no 4, 751-820 (2016).
    arXiv:1411.3578

  12. Compact Lorentzian holonomy, with Manuel Gutiérrez.
    Differential Geometry and its applications 48,11-22
    arXiv:1502.05289

  13. A note on invariant temporal functions
    Letters in Mathematical Physics 106, 959-971 (2016)
    arXiv:1502.02716

  14. Every conformal class contains a metric of bounded geometry,
    mit Marc Nardmann
    Mathematische Annalen 363, no 1, pp 143 - 174 (2015)
    arXiv:1303.5957 [math.DG]

  15. Horizons
    Advances in Theoretical and Mathematical Physics 19, no 4, pp. 747-760 (2015)
    arXiv:1111.4571 [math.DG]

  16. An invitation to Lorentzian geometry
    with Miguel Sánchez,
    Jahresbericht der Deutschen Mathematiker-Vereinigung 115 , pp. 153-183 (2014)
    arXiv:math/0604265

  17. Special temporal functions on globally hyperbolic manifolds
    Letters in Mathematical Physics 103 , no 3, pp 285-297 (2013)
    arXiv:0904.1599 [math.DG]

  18. Asymptotic flexibility of globally hyperbolic manifolds
    Comptes Rendus de l´Académie des Sciences (Mathématique) 350, no 78, pp. 421 - 423 (2012)
    arXiv:1110.1037 [math.DG]

  19. Lorentzian manifolds isometrically embeddable in Ln
    Transactions of the AMS 363, no 10, pp. 5367-5379 (2011) with Miguel Sánchez,
    arXiv:0812.4439 [math.DG]

  20. Metrizability of spaces of homomorphisms between metric vector spaces
    Journal of Geometry and Physics 60 , no 3, pp. 460-470 (2010)
    arXiv:0905.3777 [math.FA]

  21. A note on closed isometric embeddings
    Journal of Mathematical Analysis and Applications 349 , pp. 297-298 (2009)
    arXiv:0805.4657 [math.DG] DOI:10.1016/j.jmaa.2008.07.002

  22. A metric approach to Fréchet geometry
    Journal of Geometry and Physics 58 , pp. 1477-1500 (2008)
    arXiv:math/0612379 [math.DG]

  23. Codazzi spinors and globally hyperbolic manifolds with special holonomy
    with Helga Baum,
    Mathematische Zeitschrift 258, no 1 pp. 185-211 (2008)
    arXiv:0704.3725 [math.DG]

  24. The Cauchy Problem of Lorentzian Minimal Surfaces in Globally Hyperbolic Manifolds,
    Annals of Global Analysis and Geometry 32, no.1, pp. 67-85 (2007)
    arXiv:math/0210352 [math.DG]

  25. Measures in the geometric quantization of field theories
    Journal of Geometry and Physics 56, no. 6, pp. 1029-1041 (2006)


Submitted articles

  1. Gromov-Hausdorff distances for Lorentzian length spaces
    arXiv:2209.12736

  2. Functors in Lorentzian geometry: Three variations on a theme
    arXiv:2205.01617

  3. Connected holonomy is lower semi-continuous
    arXiv:2109.05572

  4. Topologies on the future causal completion
    arXiv:1909.03797

  5. Cheeger-Gromov compactness for manifolds with boundary
    arxiv:1808.06458