Liouville Energy on a Topological Two Sphere

Xiu Xiong Chen; Meijun Zhu

doi:10.1007/s40304-013-0020-8

Liouville Energy on a Topological Two Sphere

Xiu Xiong Chen
, Meijun Zhu

Mathematics

University of Oklahoma

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

2 Scopus citations

Abstract

In this paper we shall give an analytic proof of the fact that the Liouville energy on a topological two sphere is bounded from below. Our proof does not rely on the uniformization theorem and the Onofri inequality, thus it is essentially needed in the alternative proof of the uniformization theorem via the Calabi flow. Such an analytic approach also sheds light on how to obtain the boundedness for E₁ energy in the study of general Kähler manifolds.

Original language	English
Pages (from-to)	369-385
Number of pages	17
Journal	Communications in Mathematics and Statistics
Volume	1
Issue number	4
DOIs	https://doi.org/10.1007/s40304-013-0020-8
State	Published - Dec 1 2013

Keywords

Blowup analysis
Liouville energy
Moser–Trudinger–Onofri inequality
Uniformization theorem

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10.1007/s40304-013-0020-8

Cite this

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abstract = "In this paper we shall give an analytic proof of the fact that the Liouville energy on a topological two sphere is bounded from below. Our proof does not rely on the uniformization theorem and the Onofri inequality, thus it is essentially needed in the alternative proof of the uniformization theorem via the Calabi flow. Such an analytic approach also sheds light on how to obtain the boundedness for E1 energy in the study of general K{\"a}hler manifolds.",

keywords = "Blowup analysis, Liouville energy, Moser–Trudinger–Onofri inequality, Uniformization theorem",

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KW - Blowup analysis

KW - Liouville energy

KW - Moser–Trudinger–Onofri inequality

KW - Uniformization theorem

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Liouville Energy on a Topological Two Sphere

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Keywords

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