Linear stability of compact shrinking Ricci solitons
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866910389339422720 |
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| author | Cao, Huai-Dong Zhu, Meng |
| author_facet | Cao, Huai-Dong Zhu, Meng |
| contents | In this paper, we continue investigating the second variation of Perelman's $ν$-entropy for compact shrinking Ricci solitons. In particular, we improve some of our previous work in "H.-D. Cao and M. Zhu, Math. Ann. 353 (2012), No. 3, 747-763", as well as the more recent work in "M. Mehrmohamadi and A. Razavi, arXiv:2104.08343", and obtain a necessary and sufficient condition for a compact shrinking Ricci soliton to be linearly stable. Our work also extends similar results of Hamilton, Ilmanen and the first author in "arXiv:math.DG/0404165" (see also "H.-D. Cao and C. He, J. Reine Angew. Math. 2015 (2015), no. 709, 229-246.") for positive Einstein manifolds to the compact shrinking Ricci soliton case. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_01453 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Linear stability of compact shrinking Ricci solitons Cao, Huai-Dong Zhu, Meng Differential Geometry In this paper, we continue investigating the second variation of Perelman's $ν$-entropy for compact shrinking Ricci solitons. In particular, we improve some of our previous work in "H.-D. Cao and M. Zhu, Math. Ann. 353 (2012), No. 3, 747-763", as well as the more recent work in "M. Mehrmohamadi and A. Razavi, arXiv:2104.08343", and obtain a necessary and sufficient condition for a compact shrinking Ricci soliton to be linearly stable. Our work also extends similar results of Hamilton, Ilmanen and the first author in "arXiv:math.DG/0404165" (see also "H.-D. Cao and C. He, J. Reine Angew. Math. 2015 (2015), no. 709, 229-246.") for positive Einstein manifolds to the compact shrinking Ricci soliton case. |
| title | Linear stability of compact shrinking Ricci solitons |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2304.01453 |