Journal article
On a fully nonlinear elliptic equation with differential forms
Advances in mathematics (New York. 1965), Vol.454, 109867
10/2024
DOI: 10.1016/j.aim.2024.109867
Abstract
We introduce a fully nonlinear PDE with a differential form, which unifies several important equations in Kähler geometry including Monge-Ampère equations, J-equations, inverse σk equations, and deformed Hermitian Yang-Mills (dHYM) equations. We pose some natural positivity conditions on Λ, and prove analytical and algebraic criterion 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 dHYM equations with small global phase.
Details
- Title: Subtitle
- On a fully nonlinear elliptic equation with differential forms
- Creators
- Hao FangBiao Ma
- Resource Type
- Journal article
- Publication Details
- Advances in mathematics (New York. 1965), Vol.454, 109867
- Publisher
- Elsevier Inc
- DOI
- 10.1016/j.aim.2024.109867
- ISSN
- 0001-8708
- eISSN
- 1090-2082
- Grant note
We thank Jian Song and Jianchun Chu for helpful discussions. We thank Gang Tian and Xiaohua Zhu for comments and suggestions. We thank Vamsi Pritham Pingali and Ved Datar for their interest and comments.
- Language
- English
- Date published
- 10/2024
- Academic Unit
- Mathematics
- Record Identifier
- 9984691553802771
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