The Calabi flow with small initial energy

Valentino Tosatti; Ben Weinkove

doi:10.4310/mrl.2007.v14.n6.a11

The Calabi flow with small initial energy

Valentino Tosatti^*, Ben Weinkove

^*Corresponding author for this work

Mathematics

Research output: Contribution to journal › Article › peer-review

16 Scopus citations

Abstract

We show that on Kahler manifolds M with c₁(M) = 0 the Calabi flow converges to a constant scalar curvature metric if the initial Calabi energy is sufficiently small. We prove a similar result on manifolds with c ₁(M) < 0 if the Kähler class is close to the canonical class.

Original language	English (US)
Pages (from-to)	1033-1039
Number of pages	7
Journal	Mathematical Research Letters
Volume	14
Issue number	5-6
DOIs	https://doi.org/10.4310/mrl.2007.v14.n6.a11
State	Published - 2007

ASJC Scopus subject areas

General Mathematics

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title = "The Calabi flow with small initial energy",

abstract = "We show that on Kahler manifolds M with c1(M) = 0 the Calabi flow converges to a constant scalar curvature metric if the initial Calabi energy is sufficiently small. We prove a similar result on manifolds with c 1(M) < 0 if the K{\"a}hler class is close to the canonical class.",

author = "Valentino Tosatti and Ben Weinkove",

year = "2007",

doi = "10.4310/mrl.2007.v14.n6.a11",

language = "English (US)",

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AU - Tosatti, Valentino

AU - Weinkove, Ben

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N2 - We show that on Kahler manifolds M with c1(M) = 0 the Calabi flow converges to a constant scalar curvature metric if the initial Calabi energy is sufficiently small. We prove a similar result on manifolds with c 1(M) < 0 if the Kähler class is close to the canonical class.

AB - We show that on Kahler manifolds M with c1(M) = 0 the Calabi flow converges to a constant scalar curvature metric if the initial Calabi energy is sufficiently small. We prove a similar result on manifolds with c 1(M) < 0 if the Kähler class is close to the canonical class.

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DO - 10.4310/mrl.2007.v14.n6.a11

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VL - 14

SP - 1033

EP - 1039

JO - Mathematical Research Letters

JF - Mathematical Research Letters

IS - 5-6

ER -

The Calabi flow with small initial energy

Abstract

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