Mabuchi and Aubin-Yau functionals over complex manifolds

TL;DR

This paper extends the construction of Mabuchi and Aubin-Yau functionals from specific complex surfaces and three-folds to all complex manifolds of dimension two or higher, broadening their applicability.

Contribution

It introduces a method to construct Mabuchi and Aubin-Yau functionals on any complex manifold with dimension at least two, generalizing previous results.

Findings

Constructed Mabuchi and Aubin-Yau functionals for higher-dimensional complex manifolds.

Extended the applicability of these functionals beyond surfaces and three-folds.

Provided a unified approach for complex manifolds of dimension ≥ 2.

Abstract

In the previous papers \cite{L1, L2} the author constructed Mabuchi and Aubin-Yau functionals over any complex surfaces and three-folds, respectively. Using the method in \cite{L2}, we construct those functionals over any complex manifolds of the complex dimension bigger than or equal to 2.