On a fully nonlinear elliptic equation with differential forms

2023/09/27 by Fang, Hao, Ma, Biao · 3 citations
#Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2309.15451

Abstract

We introduce a fully nonlinear PDE with a differential form Λ, which unifies several important equations in Kähler geometry including Monge-Ampère equations, J-equations, inverse σ_k equations, and the deformed Hermitian Yang-Mills (dHYM) equation. We pose some natural positivity conditions on Λ, and prove analytical and algebraic criterions for the solvability of the equation. Our results generalize previous works of G.Chen, J.Song, Datar-Pingali and others. As an application, we prove a conjecture of Collins-Jacob-Yau for the dHYM equation with small global phase.

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