K-energy on polarized compactifications of Lie groups

Yan Li; Bin Zhou; Xiaohua Zhu

doi:10.1016/j.jfa.2018.04.009

K-energy on polarized compactifications of Lie groups

Yan Li, Bin Zhou, Xiaohua Zhu^*

^*Corresponding author for this work

Peking University

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

11 Citations (Scopus)

Abstract

In this paper, we study Mabuchi's K-energy on a compactification M of a reductive Lie group G, which is a complexification of its maximal compact subgroup K. We give a criterion for the properness of K-energy on the space of K×K-invariant Kähler potentials. In particular, it turns to give an alternative proof of Delcroix's theorem for the existence of Kähler–Einstein metrics in case of Fano manifolds M. We also study the existence of minimizers of K-energy for general Kähler classes of M.

Original language	English
Pages (from-to)	1023-1072
Number of pages	50
Journal	Journal of Functional Analysis
Volume	275
Issue number	5
DOIs	https://doi.org/10.1016/j.jfa.2018.04.009
Publication status	Published - 1 Sept 2018
Externally published	Yes

Keywords

Fano manifolds
K-energy
Kähler–Einstein metrics
Lie group

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10.1016/j.jfa.2018.04.009

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abstract = "In this paper, we study Mabuchi's K-energy on a compactification M of a reductive Lie group G, which is a complexification of its maximal compact subgroup K. We give a criterion for the properness of K-energy on the space of K×K-invariant K{\"a}hler potentials. In particular, it turns to give an alternative proof of Delcroix's theorem for the existence of K{\"a}hler–Einstein metrics in case of Fano manifolds M. We also study the existence of minimizers of K-energy for general K{\"a}hler classes of M.",

keywords = "Fano manifolds, K-energy, K{\"a}hler–Einstein metrics, Lie group",

author = "Yan Li and Bin Zhou and Xiaohua Zhu",

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AU - Li, Yan

AU - Zhou, Bin

AU - Zhu, Xiaohua

PY - 2018/9/1

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N2 - In this paper, we study Mabuchi's K-energy on a compactification M of a reductive Lie group G, which is a complexification of its maximal compact subgroup K. We give a criterion for the properness of K-energy on the space of K×K-invariant Kähler potentials. In particular, it turns to give an alternative proof of Delcroix's theorem for the existence of Kähler–Einstein metrics in case of Fano manifolds M. We also study the existence of minimizers of K-energy for general Kähler classes of M.

AB - In this paper, we study Mabuchi's K-energy on a compactification M of a reductive Lie group G, which is a complexification of its maximal compact subgroup K. We give a criterion for the properness of K-energy on the space of K×K-invariant Kähler potentials. In particular, it turns to give an alternative proof of Delcroix's theorem for the existence of Kähler–Einstein metrics in case of Fano manifolds M. We also study the existence of minimizers of K-energy for general Kähler classes of M.

KW - Fano manifolds

KW - K-energy

KW - Kähler–Einstein metrics

KW - Lie group

UR - http://www.scopus.com/inward/record.url?scp=85048564661&partnerID=8YFLogxK

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DO - 10.1016/j.jfa.2018.04.009

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SN - 0022-1236

VL - 275

SP - 1023

EP - 1072

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

IS - 5

ER -

K-energy on polarized compactifications of Lie groups

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Keywords

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