Stability of ALE Ricci-Flat Manifolds Under Ricci Flow

被引：0
作者：
Alix Deruelle
Klaus Kröncke
机构：
[1] Institut de mathématiques de Jussieu,Fachbereich Mathematik
[2] Universität Hamburg,undefined
来源：
The Journal of Geometric Analysis | 2021年 / 31卷
关键词：
D O I：
暂无
中图分类号：
学科分类号：
摘要：
We prove that if an ALE Ricci-flat manifold (M, g) is linearly stable and integrable, it is dynamically stable under Ricci flow, i.e. any Ricci flow starting close to g exists for all time and converges modulo diffeomorphism to an ALE Ricci-flat metric close to g. By adapting Tian’s approach in the closed case, we show that integrability holds for ALE Calabi–Yau manifolds which implies that they are dynamically stable.
引用
收藏
页码：2829 / 2870
页数：41
相关论文
共 43 条
[1]  
Anselmi D(1994)ALE manifolds and conformal field theories Int. J. Mod. Phys. A 9 3007-3057
[2]  
Billó M(2018)Scalar curvature rigidity and Ricci DeTurck flow on perturbations of Euclidean space Calc. Var. Partial Differ. Equ. 57 23-467
[3]  
Fré P(2014)Stability of hyperbolic manifolds with cusps under ricci flow Adv. Math. 263 412-450
[4]  
Zaffaroni A(2017)Heat kernel and curvature bounds in Ricci flows with bounded scalar curvature Adv. Math. 319 396-349
[5]  
Girardello L(1989)On a construction of coordinates at infinity on manifolds with fast curvature decay and maximal volume growth Invent. Math. 97 313-693
[6]  
Appleton A(1986)The mass of an asymptotically flat manifold Commun. Pure Appl. Math. 39 661-42
[7]  
Bamler RH(2001)Supersymmetric 3-branes on smooth ALE manifolds with flux Nuclear Phys. B 617 3-353
[8]  
Bamler RH(2010)Renormalization group and the Ricci flow Milan J. Math. 78 319-639
[9]  
Zhang QS(1999)-cohomologie et inégalités de Sobolev Math. Ann. 314 613-68
[10]  
Bando S(2014)A Gaussian estimate for the heat kernel on differential forms and application to the Riesz transform Math. Ann. 358 25-553
12345