Klaus Kroencke
Fachbereich Mathematik
Bereich AD
Bundesstraße 55 (Geomatikum)
20146 Hamburg

Raum 314
Tel.: +49 40 428385183
Fax: +49 40 428385190
EMail:
klaus.kroencke (at) unihamburg.de

Sprechstunden im WiSe 2020:
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:

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

Stable fixed points of the Einstein flow with positive cosmological constant (with David Fajman)
[arXiv]
To appear in: Comm. Anal. Geom. 28 (2020)

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 Ricciflat manifolds under Ricci flow (with Alix Deruelle)
[Journal, arXiv]
To appear in: J. Geom. Anal.

Stability of Einstein metrics under Ricci flow
[Journal, arXiv]
To appear in: Comm. Anal. Geom. 28 (2020) no. 2, 351394

Stable cosmological KaluzaKlein Spacetimes (with Volker Branding and David Fajman)
[Journal, arXiv]
In: Comm. Math. Phys. 368 (2019) no. 3, 10871120

Holonomy rigidity for Ricciflat metrics (with Bernd Ammann, Hartmut Weiß and Frederik Witt) [Journal, arXiv]
In: Math. Z. 291 (2019) no. 12, 303311

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 CMCEinsteinΛ flow (with David Fajman)
[Journal, arXiv]
In: Class. Quantum Grav. 35 (2018) no. 19, 195005

Global existence of Diracwave 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 sincones and coshcylinders [Journal, arXiv]
In: Ann. Sc. Norm. Super. Pisa, Cl. Sci. 18 (2018) no. 3, 11551187

Ricci flow with metric torsion on closed surfaces (with Volker Branding)
[Journal, arXiv]
In: J. Geom. Anal. 27 (2017) no. 3, 20982117

Stable and unstable Einstein warped products [Journal, arXiv]
In: Trans. Amer. Math. Soc. 369 (2017) no. 9, 65376563

The EinsteinΛ 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, 17951807

Stability and instability of Ricci solitons [Journal, arXiv]
In: Calc. Var. Partial Differ. Equ. 53 (2015) no. 12,265287

On the stability of Einstein manifolds
[Journal, arXiv]
In: Ann. Global Anal. Geom. 47 (2015) no. 12, 8198

On infinitesimal Einstein deformations
[Journal, arXiv]
In: Differ. Geom. Appl. 38 (2015) 4157
Preprints:

Spectra, stability and rigidity of sinecones
[arXiv]

L^{p}stability and positive scalar curvature rigidity of Ricciflat ALE manifolds (with Oliver Lindblad Petersen)
[arXiv]

Longtime 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, 118140

Stability of ALE Ricciflat manifolds under Ricci flow [MFO]
In: Oberwolfach Reports 14 (2017) no. 3, 22562258

Variational Stability and Rigidity of compact Einstein Manifolds [Springerlink]
F. Finster et al. (eds.) Quantum Mathematical Physics. A Bridge between Mathematics and Physics, 497513, Springer, 2016

Stability and instability of Ricci solitons [MFO]
In: Oberwolfach Reports 11 (2014) no. 3, 20172019

Scars of periodic orbits [MFO]
In: Oberwolfach Reports 8 (2011) no. 4, 2823–2825
Books:

Geometric Flows and the Geometry of Spacetime [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 [Etheses]
Diploma thesis, University of Vienna, 2010

Wave equations and Fourier integral operators on models of an expanding universe
Winter school, Konstanz, January 1517, 2020
Organizers: Klaus Kröncke (Hamburg), Jan Metzger (Potsdam), Oliver Lindblad Petersen (Hamburg)

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)

Ricci flow, mean curvature flow and related singular flows
Workshop, Hamburg, September 36, 2018
Organizers: Klaus Kröncke (Hamburg), Oliver Schnürer (Konstanz), Miles Simon (Magdeburg) and Boris Vertman (Oldenburg)

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)

Field equations on Lorentzian spacetimes
Workshop, Hamburg, March 1923, 2018
Organizers: Vicente Cortés, Sari Ghanem and Klaus Kröncke (Hamburg)

Geometric evolution equations
Winter school, Konstanz, February 59, 2018
Organizers: Klaus Kröncke (Hamburg), Oliver Schnürer (Konstanz), Miles Simon (Magdeburg) and Boris Vertman (Oldenburg)

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)

Geometric Flows and the Geometry of Spacetime
Summer School and Workshop, Hamburg, September 1923, 2016
Organizers: Vicente Cortés, Klaus Kröncke and Jan Louis (Hamburg)

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:
 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, MittagLeffler 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, MittagLeffler 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 913, 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 ParisSud
 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, BrusselsLondon 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
