关于具有微分形式的全非线性椭圆方程

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-08-02 DOI:10.1016/j.aim.2024.109867

Hao Fang, Biao Ma

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引用次数: 0

摘要

我们引入了一个具有微分形式的全非线性 PDE，它统一了凯勒几何中的几个重要方程，包括 Monge-Ampère 方程、J 方程、反 σk 方程和变形赫尔密特杨-米尔斯（dHYM）方程。我们提出了一些关于Λ的自然实在性条件，并证明了方程可解性的分析和代数准则。我们的结果概括了 G. Chen、J. Song、Datar-Pingali 等人之前的研究成果。作为应用，我们证明了柯林斯-雅各布-尤对具有小全局相位的 dHYM 方程的猜想。

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On a fully nonlinear elliptic equation with differential forms

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 $σ_{k}$ 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.

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.