Comptes Rendus
no. 9
Differential Geometry
Compact blow-up limits of finite time singularities of Ricci flow are shrinking Ricci solitons
[Les limites d'explosion compactes en temps fini de singularités du flot de Ricci sont des solitons « rapetissés »]

Présenté par : Étienne Ghys

Zhei-lei Zhang1
1 Chern Institute of Mathematics, Weijin Road 94, Tianjin 300071, PR China
Comptes Rendus. Mathématique, Volume 345 (2007) no. 9, pp. 503-506.

Utilisant les fonctionnelles λ et μ introduites par Perelman, nous démontrons que les limites d'explosion compactes, en temps fini, du flot de Ricci engendrent des singularities de type solitons « rapetissés ».

Using the λ and μ functional introduced by Perelman, we prove that the compact blow-up limit of a Ricci flow which generates singularities at finite time must be a shrinking Ricci soliton.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2007.09.017
Zhei-lei Zhang 1

1 Chern Institute of Mathematics, Weijin Road 94, Tianjin 300071, PR China 
@article{CRMATH_2007__345_9_503_0,
     author = {Zhei-lei Zhang},
     title = {Compact blow-up limits of finite time singularities of {Ricci} flow are shrinking {Ricci} solitons},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {503--506},
     publisher = {Elsevier},
     volume = {345},
     number = {9},
     year = {2007},
     doi = {10.1016/j.crma.2007.09.017},
     language = {en},
}
TY  - JOUR
AU  - Zhei-lei Zhang
TI  - Compact blow-up limits of finite time singularities of Ricci flow are shrinking Ricci solitons
JO  - Comptes Rendus. Mathématique
PY  - 2007
SP  - 503
EP  - 506
VL  - 345
IS  - 9
PB  - Elsevier
DO  - 10.1016/j.crma.2007.09.017
LA  - en
ID  - CRMATH_2007__345_9_503_0
ER  - 
%0 Journal Article
%A Zhei-lei Zhang
%T Compact blow-up limits of finite time singularities of Ricci flow are shrinking Ricci solitons
%J Comptes Rendus. Mathématique
%D 2007
%P 503-506
%V 345
%N 9
%I Elsevier
%R 10.1016/j.crma.2007.09.017
%G en
%F CRMATH_2007__345_9_503_0
Zhei-lei Zhang. Compact blow-up limits of finite time singularities of Ricci flow are shrinking Ricci solitons. Comptes Rendus. Mathématique, Volume 345 (2007) no. 9, pp. 503-506. doi : 10.1016/j.crma.2007.09.017. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2007.09.017/

[1] R.S. Hamilton Three manifolds with positive Ricci curvature, J. Differential Geom., Volume 17 (1982), pp. 255-306

[2] R.S. Hamilton A compactness property for solutions of the Ricci flow, Amer. J. Math., Volume 117 (1995), pp. 545-572

[3] T. Ivey Ricci solitons on compact three-manifolds, Differential Geom. Appl., Volume 3 (1993), pp. 301-307

[4] B. Kleiner; J. Lott Notes on Perelman's paper | arXiv

[5] G. Perelman The entropy formula for the Ricci flow and its geometric applications | arXiv

[6] O.S. Rothaus Logarithmic Sobolev inequalities and the spectrum of Schrödinger operators, J. Funct. Anal., Volume 42 (1981), pp. 110-120

Cité par Sources :

Commentaires - Politique

Ces articles pourraient vous intéresser

Remarks on compact shrinking Ricci solitons of dimension four

Li Ma

C. R. Math (2013)

Remarks on shrinking gradient Kähler–Ricci solitons with positive bisectional curvature

Guoqiang Wu; Shijin Zhang

C. R. Math (2016)

Uniqueness of asymptotic cones of complete noncompact shrinking gradient Ricci solitons with Ricci curvature decay

Bennett Chow; Peng Lu

C. R. Math (2015)