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 replace 'mullerol' with 'erasmus'.
Tel.: +49 (0) 30 2093 45435
Office: RUD25-1.308
Office hour: Thursday, 12 am to 1 pm, 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)

  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)

  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)

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

  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)

  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).

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

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

  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)

  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

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

  3. Connected holonomy is lower semi-continuous

  4. Topologies on the future causal completion

  5. Cheeger-Gromov compactness for manifolds with boundary