Stability and instability of Ricci solitons
- We consider the volume- normalized Ricci flow close to compact shrinking Ricci solitons. We show that if a compact Ricci soliton (M, g) is a local maximum of Perelman's shrinker entropy, any normalized Ricci flowstarting close to it exists for all time and converges towards a Ricci soliton. If g is not a local maximum of the shrinker entropy, we showthat there exists a nontrivial normalized Ricci flow emerging from it. These theorems are analogues of results in the Ricci- flat and in the Einstein case (Haslhofer and Muller, arXiv:1301.3219, 2013; Kroncke, arXiv: 1312.2224, 2013).
| Author details: | Klaus Kröncke |
|---|---|
| DOI: | https://doi.org/10.1007/s00526-014-0748-3 |
| ISSN: | 0944-2669 |
| ISSN: | 1432-0835 |
| Title of parent work (English): | Calculus of variations and partial differential equations |
| Publisher: | Springer |
| Place of publishing: | Heidelberg |
| Publication type: | Article |
| Language: | English |
| Year of first publication: | 2015 |
| Publication year: | 2015 |
| Release date: | 2017/03/27 |
| Volume: | 53 |
| Issue: | 1-2 |
| Number of pages: | 23 |
| First page: | 265 |
| Last Page: | 287 |
| Funding institution: | Deutsche Forschungsgemeinschaft [Sonderforschungsbereich 647] |
| Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik |
| Peer review: | Referiert |
