Kähler-Ricci flow with small initial energy

Xiuxiong Chen; Haozhao Li; Bing Wang

doi:10.1007/s00039-008-0690-7

Kähler-Ricci flow with small initial energy

Xiuxiong Chen
, Haozhao Li
, Bing Wang

Mathematics

Peking University
University of Wisconsin-Madison

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

13 Scopus citations

Abstract

In this paper, we prove that the Kähler-Ricci flow converges to a Kähler-Einstein metric when E₁ energy is small. We also prove that E₁ is bounded from below if and only if the K-energy is bounded from below in the canonical class.

Original language	English
Pages (from-to)	1525-1563
Number of pages	39
Journal	Geometric and Functional Analysis
Volume	18
Issue number	5
DOIs	https://doi.org/10.1007/s00039-008-0690-7
State	Published - Feb 2009

Keywords

Energy functionals
Kähler-einstein metrics
Kähler-Ricci flow

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10.1007/s00039-008-0690-7

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@article{33a8df3257364701ae5be37d2b012b61,

title = "K{\"a}hler-Ricci flow with small initial energy",

abstract = "In this paper, we prove that the K{\"a}hler-Ricci flow converges to a K{\"a}hler-Einstein metric when E1 energy is small. We also prove that E1 is bounded from below if and only if the K-energy is bounded from below in the canonical class.",

keywords = "Energy functionals, K{\"a}hler-einstein metrics, K{\"a}hler-Ricci flow",

author = "Xiuxiong Chen and Haozhao Li and Bing Wang",

year = "2009",

month = feb,

doi = "10.1007/s00039-008-0690-7",

language = "English",

volume = "18",

pages = "1525--1563",

journal = "Geometric and Functional Analysis",

issn = "1016-443X",

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T1 - Kähler-Ricci flow with small initial energy

AU - Chen, Xiuxiong

AU - Li, Haozhao

AU - Wang, Bing

PY - 2009/2

Y1 - 2009/2

N2 - In this paper, we prove that the Kähler-Ricci flow converges to a Kähler-Einstein metric when E1 energy is small. We also prove that E1 is bounded from below if and only if the K-energy is bounded from below in the canonical class.

AB - In this paper, we prove that the Kähler-Ricci flow converges to a Kähler-Einstein metric when E1 energy is small. We also prove that E1 is bounded from below if and only if the K-energy is bounded from below in the canonical class.

KW - Energy functionals

KW - Kähler-einstein metrics

KW - Kähler-Ricci flow

UR - https://www.scopus.com/pages/publications/84860994959

U2 - 10.1007/s00039-008-0690-7

DO - 10.1007/s00039-008-0690-7

M3 - Article

AN - SCOPUS:84860994959

SN - 1016-443X

VL - 18

SP - 1525

EP - 1563

JO - Geometric and Functional Analysis

JF - Geometric and Functional Analysis

IS - 5

ER -

Kähler-Ricci flow with small initial energy

Abstract

Keywords

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