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Linear stability of Perelman's ν-entropy on symmetric spaces of compact type

Huai-Dong Cao Lehigh University Chenxu He UC Riverside

Differential Geometry mathscidoc:1703.10008

J. Reine Angew. Math. , 709, 229–246, 2015
Following the work of Hamilton, Ilmanen and the first author [4], in this paper we study the linear stability of Perelman's ν-entropy on Einstein manifolds with positive Ricci curvature. We observe the equivalence between the linear stability (also called ν-stability in this paper) restricted to the transversal traceless symmetric 2-tensors and the stability of Einstein manifolds with respect to the Hilbert action. As a main application, we give a full classification of linear stability of the ν-entropy on symmetric spaces of compact type. In particular, we exhibit many more ν-stable and ν-unstable examples than previously known and also the first ν-stable examples, other than the standard spheres, whose second variations are negative definite.
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@inproceedings{huai-dong2015linear,
  title={Linear stability of Perelman's ν-entropy on symmetric spaces of compact type},
  author={Huai-Dong Cao, and Chenxu He},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170313112358096480667},
  booktitle={J. Reine Angew. Math. },
  volume={709},
  pages={229–246},
  year={2015},
}
Huai-Dong Cao, and Chenxu He. Linear stability of Perelman's ν-entropy on symmetric spaces of compact type. 2015. Vol. 709. In J. Reine Angew. Math. . pp.229–246. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170313112358096480667.
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