TY - JOUR
T1 - Linear stability of compact shrinking Ricci solitons
AU - Cao, Huai Dong
AU - Zhu, Meng
N1 - Publisher Copyright:
© The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2024.
PY - 2024/10
Y1 - 2024/10
N2 - 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 Cao and Zhu (Math Ann 353(3):747–763, 2012), as well as the more recent work in Mehrmohamadi and Razavi (arXiv:2104.08343, 2021), 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 Cao et al. (arXiv:math.DG/0404165, 2004) (see also Cao and He in J Reine Angew Math, 2015:229–246, 2015) for positive Einstein manifolds to the compact shrinking Ricci soliton case.
AB - 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 Cao and Zhu (Math Ann 353(3):747–763, 2012), as well as the more recent work in Mehrmohamadi and Razavi (arXiv:2104.08343, 2021), 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 Cao et al. (arXiv:math.DG/0404165, 2004) (see also Cao and He in J Reine Angew Math, 2015:229–246, 2015) for positive Einstein manifolds to the compact shrinking Ricci soliton case.
UR - https://www.scopus.com/pages/publications/85187134184
U2 - 10.1007/s00208-024-02824-w
DO - 10.1007/s00208-024-02824-w
M3 - 文章
AN - SCOPUS:85187134184
SN - 0025-5831
VL - 390
SP - 2973
EP - 2989
JO - Mathematische Annalen
JF - Mathematische Annalen
IS - 2
ER -