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.
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@article{CRMATH_2007__345_9_503_0, author = {Zhang, Zhei-lei}, 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}, url = {http://www.numdam.org/articles/10.1016/j.crma.2007.09.017/} }
TY - JOUR AU - Zhang, Zhei-lei 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 UR - http://www.numdam.org/articles/10.1016/j.crma.2007.09.017/ DO - 10.1016/j.crma.2007.09.017 LA - en ID - CRMATH_2007__345_9_503_0 ER -
%0 Journal Article %A Zhang, Zhei-lei %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 %U http://www.numdam.org/articles/10.1016/j.crma.2007.09.017/ %R 10.1016/j.crma.2007.09.017 %G en %F CRMATH_2007__345_9_503_0
Zhang, Zhei-lei. Compact blow-up limits of finite time singularities of Ricci flow are shrinking Ricci solitons. Comptes Rendus. Mathématique, Tome 345 (2007) no. 9, pp. 503-506. doi : 10.1016/j.crma.2007.09.017. http://www.numdam.org/articles/10.1016/j.crma.2007.09.017/
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