拟多次谐波包络2:蒙日-安培体积上的界

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2021-06-08 DOI:10.14231/AG-2022-021

V. Guedj, C. H. Lu

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引用次数: 10

摘要

在｛GL21a｝中，我们开发了一种新的方法来求解$L^｛infty｝$——当参考形式闭合时退化复Monge-Amp方程的先验估计。该简化假设用于确保Monge Amp ere测量的体积恒定。我们在这里研究当参考形式不再闭合时，这些体积远离零和无穷大的方式。我们建立了Grauert-Riemenschneider猜想的超越版本，部分回答了Demaily-P\u的猜想{a}un\cite｛DP04｝和Boucksom-Demaily-P\u{a}un-Peternell\引用｛BDPP13｝。我们的方法依赖于准多亚谐波包络的精细使用。本文的结果将用于求解紧致Hermitian变种上的退化复Monge-Ampere方程。

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Quasi-plurisubharmonic envelopes 2: Bounds on Monge–Ampère volumes

In \cite{GL21a} we have developed a new approach to $L^{\infty}$-a priori estimates for degenerate complex Monge-Amp\`ere equations, when the reference form is closed. This simplifying assumption was used to ensure the constancy of the volumes of Monge-Amp\`ere measures. We study here the way these volumes stay away from zero and infinity when the reference form is no longer closed. We establish a transcendental version of the Grauert-Riemenschneider conjecture, partially answering conjectures of Demailly-P\u{a}un \cite{DP04} and Boucksom-Demailly-P\u{a}un-Peternell \cite{BDPP13}. Our approach relies on a fine use of quasi-plurisubharmonic envelopes. The results obtained here will be used in \cite{GL21b} for solving degenerate complex Monge-Amp\`ere equations on compact Hermitian varieties.

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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.