Ricci flow on Kaehler-Einstein surfaces

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dc.creatorChen, Xiuxiong
dc.creatorTian, Gang
dc.date2000-10-02
dc.date2000-10-17
dc.date.accessioned2026-07-07T04:37:46Z
dc.date.available2026-07-07T04:37:46Z
dc.descriptionIn this paper, we construct a set of new functionals of Ricci curvature on any Kaehler manifolds which are invariant under holomorphic transfermations in Kaehler Einstein manifolds and essentially decreasing under the Kaehler Ricci flow. Moreover, if the initial metric has non-negative bisectional curvature, using Tian's inequality, we can prove that each of the functionals has uniform lower bound along the flow which gives a set of integral estimates on curvature. Using this set of integral estimates, we are able to show the following theorem: Let M be a Kaehler-Einstein surface with positive scalar curvature. If the initial metric has nonnegative sectional curvature and positive somewhere, then the Kaehler-Ricci flow converges exponentially fast to a Kaehler-Einstein metric with constant bisectional curvature.
dc.descriptionOne question was deleted
dc.identifierhttps://arxiv.org/abs/math/0010008
dc.identifierhttp://arxiv.org/abs/math/0010008
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/60024
dc.subjectDifferential Geometry
dc.titleRicci flow on Kaehler-Einstein surfaces
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