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Klaus Kroencke

Fachbereich Mathematik
Bereich AD
Bundesstraße 55 (Geomatikum)
20146 Hamburg 		Raum 314
Tel.: +49 40 42838-5183
Fax: +49 40 42838-5190
E-Mail: klaus.kroencke (at) uni-hamburg.de

Sprechstunden im WiSe 2020:
virtuell, nach Vereinbarung

About me:

I am an assistant professor in Mathematics at the University of Hamburg. Before I moved to Hamburg, I was a postdoc at the University of Regensburg. I obtained my PhD degree in Mathematics at the University of Potsdam under the supervision of Prof. Dr. Christian Bär, funded by the Max Planck Institute for Gravitational Physics. Previously, I did my diploma studies in Mathematics at the University of Vienna.

In the summer term 2020, I am on leave. I am a substitute professor at the University of Tübingen.

My research interests revolve around differential geometry, geometric analysis, partial differential equations and general relativity. More precisely, I am interested in special geometric structures (Einstein metrics and Ricci solitons), their stability and the structure of their moduli spaces. Moreover, I am interested in geometric flows (in particular Ricci flow) and nonlinear stability problems in general relativity.

Teaching:

SS 2020   Vorlesung: Analysis I (Universität Tübingen)
WS 2019   No teaching (research semester)
SS 2019   Lecture: Ricci flow
SS 2019   Seminar: Lorentzian geometry
WS 2018   Lecture: Advanced differential geometry
SS 2018   Vorlesung: Differentialgeometrie
WS 2017   Vorlesung: Partielle Differentialgleichungen
SS 2017   Research Seminar: Differential geometry (with Stefan Suhr)
SS 2017   Seminar: Elementare Differentialgeometrie
WS 2016   Vorlesung: Höhere Analysis
SS 2016   Lecture: Ricci flow
SS 2016   Seminar: Lorentzgeometrie
WS 2015   Lecture: Riemannian geometry

Seminar:

Publications:

  • Perelman's Entropies for Manifolds with conical Singularities (with Boris Vertman) [arXiv]
    To appear in: Trans. Amer. Math. Soc.

  • Mean curvature flow in asymptotically flat product spacetimes (with Oliver Lindblad Petersen, Felix Lubbe et al) [Journal, arXiv]
    To appear in: J. Geom. Anal.

  • Stability of ALE Ricci-flat manifolds under Ricci flow (with Alix Deruelle) [Journal, arXiv]
    To appear in: J. Geom. Anal.

  • 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]
    In: Comm. Anal. Geom. 28 (2020) no. 2, 351-394

  • Stable cosmological Kaluza-Klein Spacetimes (with Volker Branding and David Fajman) [Journal, arXiv]
    In: 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]
    In: Math. Z. 291 (2019) no. 1-2, 303-311

  • Stability of Ricci de Turck flow on Singular Spaces (with Boris Vertman) [Journal, arXiv]
    In: Calc. Var. Partial Differ. Equ. 58 (2019) no. 2, 74

  • On the CMC-Einstein-Λ flow (with David Fajman) [Journal, arXiv]
    In: 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]
    In: Calc. Var. Partial Differ. Equ. 57 (2018) no. 5, 119

  • Stability of sin-cones and cosh-cylinders [Journal, arXiv]
    In: 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]
    In: J. Geom. Anal. 27 (2017) no. 3, 2098-2117

  • Stable and unstable Einstein warped products [Journal, arXiv]
    In: Trans. Amer. Math. Soc. 369 (2017) no. 9, 6537-6563

  • The Einstein-Λ flow on product manifolds (with David Fajman) [Journal, arXiv]
    In: Class. Quant. Grav. 33 (2016) no. 23, 235018

  • Rigidity and infinitesimal deformability of Ricci solitons [Journal, arXiv]
    In: J. Geom. Anal. 26 (2016) no. 3, 1795-1807

  • Stability and instability of Ricci solitons [Journal, arXiv]
    In: Calc. Var. Partial Differ. Equ. 53 (2015) no. 1-2,265-287

  • On the stability of Einstein manifolds [Journal, arXiv]
    In: Ann. Global Anal. Geom. 47 (2015) no. 1-2, 81-98

  • On infinitesimal Einstein deformations [Journal, arXiv]
    In: Differ. Geom. Appl. 38 (2015) 41-57

Preprints:

  • Spectra, stability and rigidity of sine-cones [arXiv]

  • Lp-stability and positive scalar curvature rigidity of Ricci-flat ALE manifolds (with Oliver Lindblad Petersen) [arXiv]

  • Long-time estimates for heat flows on ALE manifolds (with Oliver Lindblad Petersen) [arXiv]

  • Bounded Ricci Curvature and Positive Scalar Curvature under Singular Ricci de Turck Flow (with Tobias Marxen and Boris Vertman) [arXiv]

  • Construction of initial data sets for Lorentzian manifolds with lightlike parallel spinors (with Bernd Ammann and Olaf Müller) [arXiv]

Conference proceedings:

  • A survey on the Ricci flow on singular spaces (with Boris Vertman) [Cambrige]
    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]
    In: 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]
    In: Oberwolfach Reports 11 (2014) no. 3, 2017-2019

  • Scars of periodic orbits [MFO]
    In: 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

Events:

Third-party projects:

Selected seminar and conference talks:

  • Dec 17, 2020, Seminar on Differential Geometry, University of Potsdam
  • Oct 21, 2020, Colloquim on Analysis, University of Freiburg
  • Aug 15, 2020, Virtual conference on Ricci and Scalar Curvature
  • Jul 03, 2020, 3rd FHST Meeting on Geometric Analysis, University of Tübingen
  • Jun 22, 2020, Seminar on Differential Geometry, University of Regensburg
  • Jun 04, 2020, Seminar on Geometric Analysis, City University of New York
  • May 18, 2020, Differential Geometry Seminar, University of Münster
  • Apr 23, 2020, Seminar on Geometric Analysis, University of Tübingen
  • Sep 25, 2019, The first Geometry Conference for Friendship of Japan and Germany, Chuo University, Tokyo
  • Sep 12, 2019, Seminar on General Relativity, Geometry and Analysis, Mittag-Leffler Institute, Stockholm
  • Jun 18, 2019, Conference on Harmonic Analysis and Spectral Theory, Technion Haifa
  • Apr 3, 2019, Conference on Geometry at Infinity, University of Münster
  • Feb 15, 2019, Workshop on Differential Geometry in the Large, Matrix Institute, Melbourne
  • Feb 8, 2019, Conference on Differential Geometry in the Large, Matrix Institute, Melbourne
  • Oct 12, 2018, Conference on Stability Phenomena in Geometry and Mathematical Physics, HU Berlin
  • Sep 21, 2018, Conference on Geometric Analysis and Mathematical Physics, University of Oldenburg
  • Sep 18, 2018, Conference on Analytical Problems in Conformal Geometry, University of Regensburg
  • May 24, 2018, Seminar on Analysis, University of Warwick
  • May 8, 2018, Conference on Geometric Analysis and Mathematical Physics, Mittag-Leffler Institute, Stockholm
  • Apr 23, 2018, Differential Geometry Seminar, University of Münster
  • Mar 5, 2018, Workshop on Geometric Evolution Equations, University of Regensburg
  • Mar 2, 2018, Seminar on Global Analysis, University of Regensburg
  • Jan 25, 2018, Seminar on Differential Geometry, University of Potsdam
  • Dec 22, 2017, 6th Christmas colloquium, Technical University of Vienna
  • Nov 24, 2017, Seminar on Nonlinear Analysis, University of Vienna
  • Oct 9-13, 2017, Summer school on Geometric Analysis on Noncompact Manifolds, University of Copenhagen
  • Oct 2, 2017, Geometry and Topology Seminar, McMaster University
  • Sep 29, 2017, Seminar on Geometric Analysis, Rutgers University
  • Sep 28, 2017, Seminar on Geometric Analysis, City University of New York
  • Sep 26, 2017, Seminar on Geometric Analysis, University of Maryland
  • Sep 14, 2017, Postdoctoral Seminar, Fields Institute, Toronto
  • Sep 6, 2017, Geometric Analysis Colloquium, Fields Institute, Toronto
  • Aug 9, 2017, Workshop on Positive Scalar Curvature, Oberwolfach
  • May 16, 2017, Seminar on Analysis and Theoretical Physics, University of Hannover
  • Apr 20, 2017, Analysis Seminar, University of Oldenburg
  • Feb 16, 2017, 7th European Relativity Seminar, University of Bremen
  • Feb 9, 2017, Colloquium of the Graduiertenkolleg, University of Regensburg
  • Dec 9, 2016, Seminar on PDE and Dynamical Systems, University of Hamburg
  • Jul 7, 2016, Seminar on Differential Geometry and Analysis, University of Hannover
  • Jun 23, 2016, Geometric Analysis Seminar, AEI Potsdam
  • Jun 10, 2016, 7th Northern German Differential Geometry Day, University of Hamburg
  • Feb 9, 2016, Seminar on Riemannian Geometry, MSRI Berkeley
  • Dec 21, 2015, Seminar on Special Holonomy, University of Regensburg
  • Nov 24, 2015, Colloquium in Pure Mathematics, University of Hamburg
  • Sep 30, 2015, Seminar on Dirac Operators, University Paris-Sud
  • Sep 22, 2015, Jahrestagung der DMV, Hamburg
  • Aug 19, 2015, Geometric Analysis Seminar, MPIM Bonn
  • May 19, 2015, Geometry Seminar, University of Munich
  • Feb 27, 2015, 5th European Relativity Seminar, Hungarian Academy of Sciences, Budapest
  • Jan 23, 2015, Brussels-London geometry seminar, University of Brussels
  • Jan 14, 2015, Geometry Seminar, University of Kiel
  • Nov 25, 2014, Geometry and Topology Seminar, University of Stuttgart
  • Aug 7, 2014, Workshop on Positive Scalar Curvature, Oberwolfach
  • May 28, 2014, Geometry and Physics Seminar, University of Vienna
  • May 13, 2014, Workshop on Kähler Geometry and Geometric Analysis, University College Cork
  • March 27, 2014, Workshop on Geometric and Singular Analysis, University of Potsdam
  • Feb 28, 2014, 4th European Relativity Seminar, ESI Vienna
  • Dec 5, 2013, Topics in Geometric Analysis Seminar, AEI Potsdam
  • Nov 6, 2013, Global Analysis and Geometry Seminar, University of Regensburg
  • Nov 4, 2013, Differential Geometry Seminar, University of Münster
  • Apr 7, 2013, Global Analysis Seminar, University of Bonn
  • Mar 8, 2013, Gravitational Physics Seminar, University of Vienna
  • Jan 28, 2013, Geometric Analysis Seminar, AEI Potsdam