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arXiv · 2309.15451

On a fully nonlinear elliptic equation with differential forms

Hao Fang·Biao Ma
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Abstract

We introduce a fully nonlinear PDE with a differential form $\Lambda$, which unifies several important equations in K\"ahler geometry including Monge-Amp\`ere equations, J-equations, inverse $\sigma_{k}$ equations, and the deformed Hermitian Yang-Mills (dHYM) equation. We pose some natural positivity conditions on $\Lambda$, 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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Hao Fang, Biao Ma. 2023-09-27. On a fully nonlinear elliptic equation with differential forms. https://arxiv.org/abs/2309.15451

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