On a fully nonlinear elliptic equation with differential forms

Hao Fang; Biao Ma

doi:10.48550/arxiv.2309.15451

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On a fully nonlinear elliptic equation with differential forms

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On a fully nonlinear elliptic equation with differential forms

Hao Fang and Biao Ma

ArXiv.org

09/27/2023

DOI: 10.48550/arxiv.2309.15451

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https://doi.org/10.48550/arxiv.2309.15451View

Preprint (Author's original)This preprint has not been evaluated by subject experts through peer review. Preprints may undergo extensive changes and/or become peer-reviewed journal articles. Open Access

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.

Details

Title: Subtitle: On a fully nonlinear elliptic equation with differential forms
Creators: Hao Fang
Biao Ma
Resource Type: Preprint
Publication Details: ArXiv.org
DOI: 10.48550/arxiv.2309.15451
ISSN: 2331-8422
Language: English
Date posted: 09/27/2023
Academic Unit: Mathematics
Record Identifier: 9984473935502771

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