Mabuchi and Aubin-Yau functionals over complex surfaces

2010/02/18 by Yi Li, Li, Yi · 1 citation
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Differential Geometry (math.DG) #FOS: Mathematics #Geometry and complex manifolds #math.DG

paper · pdf · doi:10.48550/arxiv.1002.3411

16 pages; rewrite Theorem 1.2

openalex publication_date 2010/02/18 · arxiv created 2010/03/30 · arxiv updated 2010/03/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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

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