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Publications

Preprints:

  • Dynamical Stability and Instability of Poincaré-Einstein Manifolds (with Louis Yudowitz) [arXiv]
  • A Volume-Renormalized Mass for Asymptotically Hyperbolic Manifolds (with Mattias Dahl and Stephen McCormick) [arXiv]
  • Lp cohomology and Hodge decomposition for ALE manifolds (with Baptiste Devyver) [arXiv]
  • Optimal coordinates for Ricci-flat conifolds (with Áron Szabó) [arXiv]
  • Non-degenerate Killing horizons in analytic vacuum spacetimes (with Oliver Lindblad Petersen) [arXiv]
  • Lp-stability and positive scalar curvature rigidity of Ricci-flat ALE manifolds (with Oliver Lindblad Petersen) [arXiv]

Peer-reviewed publications:

  • Local and global scalar curvature rigidity of Einstein manifolds (with Mattias Dahl) 
    [Journal, arXiv] Math. Ann. 388 (2024), no. 1, 453-510
  • Bounded Ricci Curvature and Positive Scalar Curvature under Singular Ricci de Turck Flow (with Tobias Marxen and Boris Vertman) [Journal, arXiv]
    Pac. J. Math. 324 (2023), no. 2, 295-331
  • Long-time estimates for heat flows on ALE manifolds (with Oliver Lindblad Petersen)[Journal, arXiv]
    Int. Math Res. Not. 2022 (2022), no. 24, 19943-20003
  • Construction of initial data sets for Lorentzian manifolds with lightlike parallel spinors (with Bernd Ammann and Olaf Müller)
    [Journal, arXiv] Comm. Math. Phys. 387 (2021), no. 1 , 77-109
  • Spectra, stability and rigidity of sine-cones [Journal, arXiv]
    J. Funct. Anal. 281 (2021), no. 8, 109115
  • Mean curvature flow in asymptotically flat product spacetimes (with Oliver Lindblad Petersen, Felix Lubbe et al) [Journal, arXiv]
    J. Geom. Anal. 31, (2021) no. 6, 5451–5479.
  • Perelman's Entropies for Manifolds with conical Singularities (with Boris Vertman) [Journal, arXiv]
    Trans. Amer. Math. Soc. 374 (2021) no. 4, 2873-2908
  • Stability of ALE Ricci-flat manifolds under Ricci flow (with Alix Deruelle) [Journal, arXiv]
    J. Geom. Anal. 31 (2021) no. 3, 2829-2870
  • Stable fixed points of the Einstein flow with positive cosmological constant (with David Fajman) [Journal, arXiv]
    Comm. Anal. Geom. 28 (2020) no. 7, 1533-1576
  • Stability of Einstein metrics under Ricci flow [Journal, arXiv]
    Comm. Anal. Geom. 28 (2020) no. 2, 351-394
  • Stable cosmological Kaluza-Klein Spacetimes (with Volker Branding and David Fajman) [Journal, arXiv]
    Comm. Math. Phys. 368 (2019) no. 3, 1087-1120
  • Holonomy rigidity for Ricci-flat metrics (with Bernd Ammann, Hartmut Weiß and Frederik Witt) [Journal, arXiv]
    Math. Z. 291 (2019) no. 1-2, 303-311
  • Stability of Ricci de Turck flow on Singular Spaces (with Boris Vertman) [Journal, arXiv]
    Calc. Var. Partial Differ. Equ. 58 (2019) no. 2, 74
  • On the CMC-Einstein-Λ flow (with David Fajman) [Journal, arXiv]
    Class. Quantum Grav. 35 (2018) no. 19, 195005
  • Global existence of Dirac-wave maps with curvature term on expanding spacetimes (with Volker Branding) [Journal, arXiv]
    Calc. Var. Partial Differ. Equ. 57 (2018) no. 5, 119
  • Stability of sin-cones and cosh-cylinders [Journal, arXiv]
    Ann. Sc. Norm. Super. Pisa, Cl. Sci. 18 (2018) no. 3, 1155-1187
  • Ricci flow with metric torsion on closed surfaces (with Volker Branding) [Journal, arXiv]
    J. Geom. Anal. 27 (2017) no. 3, 2098-2117
  • Stable and unstable Einstein warped products [Journal, arXiv]
    Trans. Amer. Math. Soc. 369 (2017) no. 9, 6537-6563
  • The Einstein-Λ flow on product manifolds (with David Fajman) [Journal, arXiv]
    Class. Quant. Grav. 33 (2016) no. 23, 235018
  • Rigidity and infinitesimal deformability of Ricci solitons [Journal, arXiv]
    J. Geom. Anal. 26 (2016) no. 3, 1795-1807
  • Stability and instability of Ricci solitons [Journal, arXiv]
    Calc. Var. Partial Differ. Equ. 53 (2015) no. 1-2,265-287
  • On the stability of Einstein manifolds [Journal, arXiv]
    Ann. Global Anal. Geom. 47 (2015) no. 1-2, 81-98
  • On infinitesimal Einstein deformations [Journal, arXiv]
    Differ. Geom. Appl. 38 (2015) 41-57

Conference proceedings:

  • Lp-stability and positive scalar curvature rigidity of Ricci-flat ALE manifolds [MFO]
    Oberwolfach Reports 18 (2021) no. 2, 1618-1621
  • A survey on the Ricci flow on singular spaces (with Boris Vertman) [Cambrige, arXiv]
    O. Dearricott et al. (eds.) Differential Geometry in the Large, Cambridge University Press. 463, 118-140
  • Stability of ALE Ricci-flat manifolds under Ricci flow [MFO]
    Oberwolfach Reports 14 (2017) no. 3, 2256-2258
  • Variational Stability and Rigidity of compact Einstein Manifolds [Springerlink]
    F. Finster et al. (eds.) Quantum Mathematical Physics. A Bridge between Mathematics and Physics, 497-513, Springer, 2016
  • Stability and instability of Ricci solitons [MFO]
    Oberwolfach Reports 11 (2014) no. 3, 2017-2019
  • Scars of periodic orbits [MFO]
    Oberwolfach Reports 8 (2011) no. 4, 2823–2825

Books:

  • Geometric Flows and the Geometry of Space-time [Springerlink]
    Editors: Vicente Cortés, Klaus Kröncke, Jan Louis
    Tutorials, Schools, and Workshops in the Mathematical Sciences, Birkhäuser, 2018

Theses:

  • Stability of Einstein Manifolds [OPUS]
    Doctoral thesis, University of Potsdam, 2013
  • Comparison theorems in Riemannian geometry [E-theses]
    Diploma thesis, University of Vienna, 2010