@phdthesis{Kroencke2013,
  author    = {Kr{\"o}ncke, Klaus},
  title     = {Stability of Einstein Manifolds},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-69639},
  school      = {Universit{\"a}t Potsdam},
  year      = {2013},
  abstract  = {This thesis deals with Einstein metrics and the Ricci flow on compact mani- folds. We study the second variation of the Einstein-Hilbert functional on Ein- stein metrics. In the first part of the work, we find curvature conditions which ensure the stability of Einstein manifolds with respect to the Einstein-Hilbert functional, i.e. that the second variation of the Einstein-Hilbert functional at the metric is nonpositive in the direction of transverse-traceless tensors. The second part of the work is devoted to the study of the Ricci flow and how its behaviour close to Einstein metrics is influenced by the variational be- haviour of the Einstein-Hilbert functional. We find conditions which imply that Einstein metrics are dynamically stable or unstable with respect to the Ricci flow and we express these conditions in terms of stability properties of the metric with respect to the Einstein-Hilbert functional and properties of the Laplacian spectrum.},
  language  = {en}
}
@article{Kroencke2015,
  author    = {Kroencke, Klaus},
  title     = {On the stability of Einstein manifolds},
  series = {Annals of global analysis and geometry},
  volume    = {47},
  journal   = {Annals of global analysis and geometry},
  number    = {1},
  publisher = {Springer},
  address   = {Dordrecht},
  issn      = {0232-704X},
  doi       = {10.1007/s10455-014-9436-y},
  pages     = {81 -- 98},
  year      = {2015},
  abstract  = {Certain curvature conditions for the stability of Einstein manifolds with respect to the Einstein-Hilbert action are given. These conditions are given in terms of quantities involving the Weyl tensor and the Bochner tensor. In dimension six, a stability criterion involving the Euler characteristic is given.},
  language  = {en}
}