[Le flot de Ricci sur une variété kählérienne compacte à courbure bisectionnelle positive]
Cette Note annonce une nouvelle démonstration de l'estimée uniforme de la courbure des métriques solutions du flot de Ricci sur une variété kählérienne compacte à courbure bisectionnelle positive. La démonstration proposée ne suppose pas l'existence d'une métrique d'Einstein–Kähler sur la variété, contrairement à un travail récent de XiuXiong Chen et de Gang Tian. Elle s'appuie sur l'inégalité de Harnack pour le flot de Ricci–Kähler (voir Invent. Math. 10 (1992) 247–263), et aussi sur une estimation du rayon d'injectivité du flot de Ricci obtenue récemment par Perelman.
This Note announces a new proof of the uniform estimate on the curvature of metric solutions to the Ricci flow on a compact Kähler manifold with positive bisectional curvature. This proof does not pre-suppose the existence of a Kähler–Einstein metric on the manifold, unlike the recent work of XiuXiong Chen and Gang Tian. It is based on the Harnack inequality for the Ricci–Kähler flow (see Invent. Math. 10 (1992) 247–263), and also on an estimation of the injectivity radius for the Ricci flow, obtained recently by Perelman.
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@article{CRMATH_2003__337_12_781_0,
author = {Huai-Dong Cao and Bing-Long Chen and Xi-Ping Zhu},
title = {Ricci flow on compact {K\"ahler} manifolds of positive bisectional curvature},
journal = {Comptes Rendus. Math\'ematique},
pages = {781--784},
publisher = {Elsevier},
volume = {337},
number = {12},
year = {2003},
doi = {10.1016/j.crma.2003.09.030},
language = {en},
}
TY - JOUR AU - Huai-Dong Cao AU - Bing-Long Chen AU - Xi-Ping Zhu TI - Ricci flow on compact Kähler manifolds of positive bisectional curvature JO - Comptes Rendus. Mathématique PY - 2003 SP - 781 EP - 784 VL - 337 IS - 12 PB - Elsevier DO - 10.1016/j.crma.2003.09.030 LA - en ID - CRMATH_2003__337_12_781_0 ER -
Huai-Dong Cao; Bing-Long Chen; Xi-Ping Zhu. Ricci flow on compact Kähler manifolds of positive bisectional curvature. Comptes Rendus. Mathématique, Volume 337 (2003) no. 12, pp. 781-784. doi : 10.1016/j.crma.2003.09.030. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2003.09.030/
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