A Characterization of the Unit Ball by a Kähler–Einstein Potential

Young Jun Choi; Kang Hyurk Lee; Aeryeong Seo

doi:10.1007/s12220-022-01174-w

A Characterization of the Unit Ball by a Kähler–Einstein Potential

Young Jun Choi, Kang Hyurk Lee, Aeryeong Seo

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

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Abstract

We will show that a universal covering of a compact Kähler manifold with ample canonical bundle is the unit ball if it admits a global potential function of the Kähler–Einstein metric whose gradient length is a minimal constant. As an application, we will extend the Wong–Rosay theorem to a complex manifold without boundary.

Original language	English
Article number	133
Journal	Journal of Geometric Analysis
Volume	33
Issue number	4
DOIs	https://doi.org/10.1007/s12220-022-01174-w
State	Published - Apr 2023

Keywords

Automorphism groups
Complete holomorphic vector fields
The Kähler–Einstein metric
The unit ball

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10.1007/s12220-022-01174-w

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abstract = "We will show that a universal covering of a compact K{\"a}hler manifold with ample canonical bundle is the unit ball if it admits a global potential function of the K{\"a}hler–Einstein metric whose gradient length is a minimal constant. As an application, we will extend the Wong–Rosay theorem to a complex manifold without boundary.",

keywords = "Automorphism groups, Complete holomorphic vector fields, The K{\"a}hler–Einstein metric, The unit ball",

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AU - Seo, Aeryeong

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N2 - We will show that a universal covering of a compact Kähler manifold with ample canonical bundle is the unit ball if it admits a global potential function of the Kähler–Einstein metric whose gradient length is a minimal constant. As an application, we will extend the Wong–Rosay theorem to a complex manifold without boundary.

AB - We will show that a universal covering of a compact Kähler manifold with ample canonical bundle is the unit ball if it admits a global potential function of the Kähler–Einstein metric whose gradient length is a minimal constant. As an application, we will extend the Wong–Rosay theorem to a complex manifold without boundary.

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KW - Complete holomorphic vector fields

KW - The Kähler–Einstein metric

KW - The unit ball

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A Characterization of the Unit Ball by a Kähler–Einstein Potential

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Keywords

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