Mabuchi and Aubin-Yau functionals over complex three-folds

Details Mabuchi and Aubin-Yau functionals over complex three-folds Mabuchi and Aubin-Yau functionals over complex three-folds

2010-03-27

arxiv.org/abs/1003.5307v1

Mathematics

Differential Geometry

24 pages

Scientific paper

In this paper we construct Mabuchi $\mathcal{L}^{{\rm M}}_{\omega}$ functional and Aubin-Yau functionals $\mathcal{I}^{{\rm AY}}_{\omega}, \mathcal{J}^{{\rm AY}}_{\omega}$ on any compact complex three-folds. The method presented here will be used in the forthcoming paper \cite{L1} on the construction of those functionals on any compact complex manifolds, which generalizes the previous work \cite{L}.

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