50 citations · 159 across the 16 of their papers we have counts for
19 papers
Dynamical Stability and Instability of Poincaré--Einstein Manifolds
Klaus Kroencke, Louis Yudowitz
We prove dynamical stability and instability theorems for Poincaré-Einstein metrics under the Ricci flow. Our key tool is a variant of the expander entropy for asymptotically hyper…
A volume-renormalized mass for asymptotically hyperbolic manifolds
Mattias Dahl, Klaus Kroencke, Stephen McCormick
We define a geometric quantity for asymptotically hyperbolic manifolds, which we call the volume-renormalized mass. It is essentially a linear combination of the ADM mass surface i…
The asymptotic expansion of the spacetime metric at the event horizon
Klaus Kroencke, Oliver Petersen
Hawking's local rigidity theorem, proven in the smooth setting by Alexakis-Ionescu-Klainerman, says that the event horizon of any stationary non-extremal black hole is a non-degene…
Local and global scalar curvature rigidity of Einstein manifolds
Mattias Dahl, Klaus Kroencke
An Einstein manifold is called scalar curvature rigid if there are no compactly supported volume-preserving deformation of the metric which increase the scalar curvature. We give v…
Convergence of the Ricci flow to Ricci-flat ALE manifolds and positive scalar curvature rigidity
Klaus Kroencke, Oliver Lindblad Petersen
We prove stability of integrable ALE manifolds with a parallel spinor under Ricci flow, given an initial metric which is close in , for any , where…
Bounded Ricci Curvature and Positive Scalar Curvature under Singular Ricci de Turck Flow
Klaus Kroencke, Tobias Marxen, Boris Vertman
In this paper we consider a Ricci de Turck flow of spaces with isolated conical singularities, which preserves the conical structure along the flow. We establish that a given initi…
Construction of initial data sets for Lorentzian manifolds with lightlike parallel spinors
Bernd Ammann, Klaus Kroencke, Olaf Müller
Lorentzian manifolds with parallel spinors are important objects of study in several branches of geometry, analysis and mathematical physics. Their Cauchy problem has recently been…
Global existence of Dirac-wave maps with curvature term on expanding spacetimes
Volker Branding, Klaus Kroencke
We prove the global existence of Dirac-wave maps with curvature term with small initial data on globally hyperbolic manifolds of arbitrary dimension which satisfy a suitable growth…
Stability of ALE Ricci-flat manifolds under Ricci flow
Alix Deruelle, Klaus Kroencke
We prove that if an ALE Ricci-flat manifold is linearly stable and integrable, it is dynamically stable under Ricci flow, i.e. any Ricci flow starting close to g exists for…
The Einstein-Lambda flow on product manifolds
David Fajman, Klaus Kroencke
We consider the vacuum Einstein flow with a positive cosmological constant on spatial manifolds of product form. In spatial dimension at least four we show the existence of continu…
The Ricci flow with metric torsion on closed surfaces
Volker Branding, Klaus Kroencke
The famous Uniformization Theorem states that on closed Riemannian surfaces there always exists a metric of constant curvature for the Levi-Cevita connection. In this article we pr…
Holonomy rigidity for Ricci-flat metrics
Bernd Ammann, Klaus Kroencke, Hartmut Weiss +1
On a closed connected oriented manifold we study the space of all Riemannian metrics which admit a non-zero parallel spinor on the universal covering. Such…
On infinitesimal Einstein deformations
Klaus Kroencke
We study infinitesimal Einstein deformations on compact flat manifolds and on product manifolds. Moreover, we prove refinements of results by Koiso and Bourguignon which yield obst…
Stable and unstable Einstein warped products
Klaus Kroencke
In this article, we systematically investigate the stability properties of certain warped product Einstein manifolds. We characterize stability of these metrics in terms of an eige…
Stable fixed points of the Einstein flow with positive cosmological constant
David Fajman, Klaus Kroencke
We prove nonlinear stability for a large class of solutions to the Einstein equations with a positive cosmological constant and compact spatial topology in arbitrary dimensions, wh…
Rigidity and infinitesimal deformability of Ricci solitons
Klaus Kroencke
In this paper, an obstruction against the integrability of certain infinitesimal solitonic deformations is given. Using this obstruction, we show that the complex projective spaces…
Stability and instability of Ricci solitons
Klaus Kroencke
We consider the volume-normalized Ricci flow close to compact shrinking Ricci solitons. We show that if a compact Ricci soliton is a local maximum of Perelman's shrinker en…
Stability of Einstein metrics under Ricci flow
Klaus Kroencke
We prove dynamical stability and instability theorems for compact Einstein metrics under the Ricci flow. We give a nearly complete charactarization of dynamical stability and insta…
On the stability of Einstein manifolds
Klaus Kroencke
Certain curvature conditions for stability of Einstein manifolds with respect to the Einstein-Hilbert action are given. These conditions are given in terms of quantities involving…