摘要
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.
基金
We thank Yuxiang Li for pointing out the proof of Lemma 3.5 in an early version is incomplete.We also thank the referee for the careful reviewing and comments.
