List of Publications

Preprints

• Global hyperbolicity through the eyes of the null distance [arXiv, pdf]
  with Leonardo García-Heveling, Sep 2022, 34 p.

• Time functions on Lorentzian length spaces [arXiv, pdf]
  with Leonardo García-Heveling, Aug 2021, 39 p.

Peer-reviewed articles

• Properties of the null distance and spacetime convergence [arXiv, pdf, journal]
  with Brian Allen, Int. Math. Res. Not. IMRN 2022, no. 10, 7729–7808.

• Variations of Weyl’s tube formula [arXiv, pdf, journal]
  with Gert Heckman, J. Geom. Anal. 31 (2021), no. 12, 11952–11970.

• Weak second Bianchi identity for static, spherically symmetric spacetimes with timelike singularities [arXiv, pdf, journal]
  with Michael K.-H. Kiessling and A. Shadi Tahvildar-Zadeh, Classical Quantum Gravity 38 (2021), no. 18, 185001, 31 p.

• Inscribed radius bounds for lower Ricci bounded metric measure spaces with mean convex boundary [arXiv, pdf, journal]
  with Christian Ketterer, Robert J. McCann, and Eric Woolgar, SIGMA Symmetry Integrability Geom. Methods Appl. 16 (2020), 131, 29 p. (Special Issue on Scalar and Ricci Curvature in honor of Misha Gromov on his 75th Birthday)

• Initial data and black holes for matter models [arXiv, pdf, book]
  in “Hyperbolic Problems: Theory, Numerics, Applications”, by Alberto Bressan, Marta Lewicka, Dehua Wang, Yuxi Zheng (Eds.), AIMS Ser. Appl. Math., vol. 10, 336–345, Am. Inst. Math. Sci. (AIMS), Springfield, MO, 2020.

• On the asymptotic behavior of static perfect fluids [arXiv, pdf, journal]
  with Lars Andersson, Ann. Henri Poincaré 20 (2019), no. 3, 813–857.

• Hyperboloidal evolution and global dynamics for the focusing cubic wave equation [arXiv, pdf, journal]
  with Roland Donninger, Comm. Math. Phys. 353 (2017), no. 2, 549–596.

• Length structures on manifolds with continuous Riemannian metrics [arXiv, pdf, journal]
  New York J. Math. 21 (2015), 273–296.

• The formation of trapped surfaces in spherically-symmetric Einstein-Euler spacetimes with bounded variation [arXiv, pdf, journal]
  with Philippe G. LeFloch, J. Math. Pures Appl. 102 (2014), no. 6, 1164–1217.

• New energy inequalities for tensorial wave equations on spacetimes that satisfy a one-sided bound [arXiv, pdf, journal]
  with James D.E. Grant and Philippe G. LeFloch, Comm. Partial Differential Equations 37 (2012), no. 9, 1596–1619.

• Tectonic geomorphological investigations of antiforms using differential geometry: Permam Anticline, northern Iraq [pdf, journal]
  with Marcel Frehner and Bernhard Grasemann, AAPG Bulletin 96 (2012), no. 2, 301–314.

• Algebras of generalized functions with smooth parameter dependence [arXiv, pdf, journal]
  with Michael Kunzinger, Proc. Edinburgh Math. Soc. (2) 55 (2012), no. 1, 105–124.

• An algebraic approach to manifold-valued generalized functions [arXiv, pdf, journal]
  Monatsh. Math. 166 (2012), no. 3-4, 361–370.

Non peer-reviewed articles, reports etc.

• Matter particles, naked singularities, and a weak second Bianchi identity [pdf, report, workshop]
  Oberwolfach Rep. 18 (2021), no. 3, 2231–2233.

• Singularity formation for perfect fluids with linear equation of state [pdf, report, workshop]
  Oberwolfach Rep. 17 (2020), no. 4, 2104–2106.

• LehrFEM – A 2D Finite Element Toolbox [pdf]
  with contributions by Patrick Meury and Eivind Fonn, Manual for FEM MATLAB code (Sep 2008), ETH Zürich, 118 p.

Theses

• Analytic and geometric aspects of spacetimes of low regularity [german abstract, french abstract, multilingual abstract, full version on request]
  PhD thesis in Mathematics (2014), Université Pierre et Marie Curie (Paris 6) and University of Vienna.

• Curvature analysis of anticlines in the Zagros mountains (Iraq) [abstract, pdf, MATLAB code]
  Bachelor thesis in Earth Sciences (2010), University of Vienna.

• Isomorphisms of algebras of smooth and generalized functions [abstract, pdf]
  Diploma/Master thesis in Mathematics (2009), University of Vienna.

Lecture notes

• Introduction to Riemannian Geometry [pdf] (3rd year Bachelor, version 2021/22, 141 p.)

• Introduction to Partial Differential Equations [pdf] (3rd year Bachelor, version 2020/21, 96 p.)

• Optimization in Geometry and Physics [pdf] (2nd year Bachelor, version 2020/21, 57 p.)