Liouville Energy on a Topological Two Sphere

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 E ₁ energy in the study of general Kähler manifolds.

Keywords

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

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