TY - JOUR
T1 - On second variation of Perelman's Ricci shrinker entropy
AU - Cao, Huai Dong
AU - Zhu, Meng
PY - 2012/7
Y1 - 2012/7
N2 - In this paper we provide a detailed proof of the second variation formula, essentially due to Richard Hamilton, Tom Ilmanen and the first author, for Perelman's ν-entropy. In particular, we correct an error in the stability operator stated in Theorem 6. 3 of (Cao in Adv Lect Math 11:1-38, 2010). Moreover, we obtain a necessary condition for linearly stable shrinkers in terms of the least eigenvalue and its multiplicity of certain Lichnerowicz type operator associated to the second variation.
AB - In this paper we provide a detailed proof of the second variation formula, essentially due to Richard Hamilton, Tom Ilmanen and the first author, for Perelman's ν-entropy. In particular, we correct an error in the stability operator stated in Theorem 6. 3 of (Cao in Adv Lect Math 11:1-38, 2010). Moreover, we obtain a necessary condition for linearly stable shrinkers in terms of the least eigenvalue and its multiplicity of certain Lichnerowicz type operator associated to the second variation.
UR - https://www.scopus.com/pages/publications/84861345777
U2 - 10.1007/s00208-011-0701-0
DO - 10.1007/s00208-011-0701-0
M3 - 文章
AN - SCOPUS:84861345777
SN - 0025-5831
VL - 353
SP - 747
EP - 763
JO - Mathematische Annalen
JF - Mathematische Annalen
IS - 3
ER -