Logarithmic Hardy-Littlewood-Sobolev inequality on pseudo-Einstein 3-manifolds and the logarithmic Robin mass

IF 0.8 3区数学 Q2 MATHEMATICS

Publicacions Matematiques Pub Date : 2019-11-17 DOI:10.5565/publmat6722302

Ali Maalaoui

引用次数: 3

Abstract

Given a three dimensional pseudo-Einstein CR manifold $(M,T^{1,0}M,\theta)$, we study the existence of a contact structure conformal to $\theta$ for which the logarithmic Hardy-Littlewood-Sobolev (LHLS) inequality holds. Our approach closely follows \cite{Ok1} in the Riemannian setting. For this purpose, we introduce the notion of Robin mass as the constant term appearing in the expansion of the Green's function of the $P'$-operator. We show that the LHLS inequality appears when we study the variation of the total mass under conformal change. Then we exhibit an Aubin type result guaranteeing the existence of a minimizer for the total mass which yields the classical LHLS inequality.

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伪爱因斯坦3-流形上的对数Hardy-Littlewood-Sobolev不等式和对数Robin质量

给定一个三维拟Einstein CR流形$（M，T^{1,0}M，θ）$，我们研究了对数Hardy-Littlewood-Sobolev（LHLS）不等式成立的与$θ$共形的接触结构的存在性。我们的方法密切遵循黎曼环境中的引用｛Ok1｝。为此，我们引入了Robin质量的概念，作为$P'$-算子的Green函数展开中出现的常数项。我们证明了当我们研究保角变化下总质量的变化时，LHLS不等式出现了。然后，我们给出了一个Aubin型结果，保证了总质量的极小值的存在，这产生了经典的LHLS不等式。

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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来源期刊

Publicacions Matematiques 数学-数学

CiteScore

1.60

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Publicacions Matemàtiques is a research mathematical journal published by the Department of Mathematics of the Universitat Autònoma de Barcelona since 1976 (before 1988 named Publicacions de la Secció de Matemàtiques, ISSN: 0210-2978 print, 2014-4369 online). Two issues, constituting a single volume, are published each year. The journal has a large circulation being received by more than two hundred libraries all over the world. It is indexed by Mathematical Reviews, Zentralblatt Math., Science Citation Index, SciSearch®, ISI Alerting Services, COMPUMATH Citation Index®, and it participates in the Euclid Project and JSTOR. Free access is provided to all published papers through the web page. Publicacions Matemàtiques is a non-profit university journal which gives special attention to the authors during the whole editorial process. In 2019, the average time between the reception of a paper and its publication was twenty-two months, and the average time between the acceptance of a paper and its publication was fifteen months. The journal keeps on receiving a large number of submissions, so the authors should be warned that currently only articles with excellent reports can be accepted.