Mabuchi and Aubin-Yau functionals over complex surfaces

Abstract

In this note we construct Mabuchi ${\mathcal{L}}_{\omega }^{\mathrm{M}}$ functional and Aubin-Yau functionals ${\mathcal{I}}_{\omega }^{\mathrm{AY}},{\mathcal{J}}_{\omega }^{\mathrm{AY}}$ on any compact complex surfaces, and establish a number of properties. Our construction coincides with the original one in the Kähler case.

16 pages; rewrite Theorem 1.2

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