仿射最大类型方程的不变量

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY Accounts of Chemical Research Pub Date : 2024-09-23 DOI:10.1016/j.jmaa.2024.128898

Zhao Lian

引用次数: 0

摘要

设 y:M→Rn+1 是光滑连通流形向实仿射空间 Rn+1 的局部强凸超曲面浸入，是定义在域 Ω⊂Rn 上的光滑严格凸函数 xn+1=f(x1,...,xn) 的图。考虑到凸函数 f 图的α 相关归一化，我们将证明一类仿射最大型非线性四阶偏微分方程的伯恩斯坦定理。作为应用，我们定义了方程的不变式，并证明了在 n≤5 时，复环 (C⁎)n 上具有消失标量曲率的完整 Tn 不变凯勒度量的刚性结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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An invariant for affine maximal type equations

Let

y : M \to R^{n + 1}

be a locally strongly convex hypersurface immersion of a smooth, connected manifold into the real affine space

R^{n + 1}

, given as the graph of a smooth, strictly convex function

x_{n + 1} = f (x_{1}, . . ., x_{n})

defined on a domain

Ω \subset R^{n}

. Considering the α-relative normalization of the graph of the convex function f, we will prove a Bernstein theorem for a class of nonlinear, fourth order partial differential equations of affine maximal type. As applications, we define an invariant of the equations and prove a rigidity result of the complete

T^{n}

-invariant Kähler metric on complex torus

{(C^{⁎})}^{n}

with vanishing scalar curvature for

n \leq 5

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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.

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