Klaus Kroencke
Fachbereich Mathematik
Bereich AD
Bundesstraße 55 (Geomatikum)
20146 Hamburg
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Raum 314
Tel.: +49 40 42838-5183
Fax: +49 40 42838-5190
E-Mail:
klaus.kroencke (at) uni-hamburg.de
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Sprechstunden im WiSe 2018:
virtuell, nach Vereinbarung
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.
Seminar:
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Perelman's Entropies for Manifolds with conical Singularities (with Boris Vertman)
[arXiv]
To appear in: Trans. Amer. Math. Soc.
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Stable fixed points of the Einstein flow with positive cosmological constant (with David Fajman)
[arXiv]
To appear in: Comm. Anal. Geom. 28 (2020)
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Mean curvature flow in asymptotically flat product spacetimes (with Oliver Lindblad Petersen, Felix Lubbe et al)
[Journal, arXiv]
To appear in: J. Geom. Anal.
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Stability of ALE Ricci-flat manifolds under Ricci flow (with Alix Deruelle)
[Journal, arXiv]
To appear in: J. Geom. Anal.
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Stability of Einstein metrics under Ricci flow
[Journal, arXiv]
To appear in: Comm. Anal. Geom. 28 (2020) no. 2, 351-394
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Stable cosmological Kaluza-Klein Spacetimes (with Volker Branding and David Fajman)
[Journal, arXiv]
In: Comm. Math. Phys. 368 (2019) no. 3, 1087-1120
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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
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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
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On the CMC-Einstein-Λ flow (with David Fajman)
[Journal, arXiv]
In: Class. Quantum Grav. 35 (2018) no. 19, 195005
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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
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Stability of sin-cones and cosh-cylinders [Journal, arXiv]
In: Ann. Sc. Norm. Super. Pisa, Cl. Sci. 18 (2018) no. 3, 1155-1187
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Ricci flow with metric torsion on closed surfaces (with Volker Branding)
[Journal, arXiv]
In: J. Geom. Anal. 27 (2017) no. 3, 2098-2117
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Stable and unstable Einstein warped products [Journal, arXiv]
In: Trans. Amer. Math. Soc. 369 (2017) no. 9, 6537-6563
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The Einstein-Λ flow on product manifolds (with David Fajman)
[Journal, arXiv]
In: Class. Quant. Grav. 33 (2016) no. 23, 235018
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Rigidity and infinitesimal deformability of Ricci solitons
[Journal, arXiv]
In: J. Geom. Anal. 26 (2016) no. 3, 1795-1807
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Stability and instability of Ricci solitons [Journal, arXiv]
In: Calc. Var. Partial Differ. Equ. 53 (2015) no. 1-2,265-287
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On the stability of Einstein manifolds
[Journal, arXiv]
In: Ann. Global Anal. Geom. 47 (2015) no. 1-2, 81-98
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On infinitesimal Einstein deformations
[Journal, arXiv]
In: Differ. Geom. Appl. 38 (2015) 41-57
Preprints:
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Lp-stability and positive scalar curvature rigidity of Ricci-flat ALE manifolds (with Oliver Lindblad Petersen)
[arXiv]
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Long-time estimates for heat flows on ALE manifolds (with Oliver Lindblad Petersen)
[arXiv]
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Bounded Ricci Curvature and Positive Scalar Curvature under Singular Ricci de Turck Flow (with Tobias Marxen and Boris Vertman)
[arXiv]
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Construction of initial data sets for Lorentzian manifolds with lightlike parallel spinors (with Bernd Ammann and Olaf Müller)
[arXiv]
Conference proceedings:
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Stability of ALE Ricci-flat manifolds under Ricci flow [MFO]
In: Oberwolfach Reports 14 (2017) no. 3, 2256-2258
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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
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Stability and instability of Ricci solitons [MFO]
In: Oberwolfach Reports 11 (2014) no. 3, 2017-2019
Books:
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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
- Stability of Einstein Manifolds [OPUS]
Doctoral thesis, University of Potsdam, 2013
- Comparison theorems in Riemannian geometry [E-theses]
Diploma thesis, University of Vienna, 2010
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Wave equations and Fourier integral operators on models of an expanding universe
Winter school, Konstanz, January 15-17, 2020
Organizers: Klaus Kröncke (Hamburg), Jan Metzger (Potsdam), Oliver Lindblad Petersen (Hamburg)
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10th Northern German Differential Geometry Day
Hamburg, June 21, 2019
Organizers: Roger Bielawski, Lynn Heller and Knut Smoczyk
(Hannover), Vicente Cortés and Klaus Kröncke (Hamburg), Jens Heber and Hartmut Weiß (Kiel)
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Ricci flow, mean curvature flow and related singular flows
Workshop, Hamburg, September 3-6, 2018
Organizers: Klaus Kröncke (Hamburg), Oliver Schnürer (Konstanz), Miles Simon (Magdeburg) and Boris Vertman (Oldenburg)
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9th Northern German Differential Geometry Day
Kiel, June 8, 2018
Organizers: Roger Bielawski, Lynn Heller and Knut Smoczyk
(Hannover), Vicente Cortés and Klaus Kröncke (Hamburg), Jens Heber and Hartmut Weiß (Kiel)
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Field equations on Lorentzian space-times
Workshop, Hamburg, March 19-23, 2018
Organizers: Vicente Cortés, Sari Ghanem and Klaus Kröncke (Hamburg)
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Geometric evolution equations
Winter school, Konstanz, February 5-9, 2018
Organizers: Klaus Kröncke (Hamburg), Oliver Schnürer (Konstanz), Miles Simon (Magdeburg) and Boris Vertman (Oldenburg)
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8th Northern German Differential Geometry Day
Hannover, June 30, 2017
Organizers: Roger Bielawski and Knut Smoczyk
(Hannover), Vicente Cortés and Klaus Kröncke (Hamburg), Jens Heber and Hartmut Weiß (Kiel)
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Geometric Flows and the Geometry of Space-time
Summer School and Workshop, Hamburg, September 19-23, 2016
Organizers: Vicente Cortés, Klaus Kröncke and Jan Louis (Hamburg)
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7th Northern German Differential Geometry Day
Hamburg, June 10, 2016
Organizers: Roger Bielawski and Knut Smoczyk
(Hannover), Vicente Cortés and Klaus Kröncke (Hamburg), Jens Heber and Hartmut Weiß (Kiel)
Selected seminar and conference talks:
- 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
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