具有正常数边界平均曲率的负常数标量曲率共形度量的先验估计

IF 1 2区数学 Q1 MATHEMATICS

Journal of the London Mathematical Society-Second Series Pub Date : 2025-02-28 DOI:10.1112/jlms.70109

Sérgio Almaraz, Shaodong Wang

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引用次数: 0

摘要

在具有边界的紧黎曼流形上，研究了内部为负常数标量曲率，边界为正常数平均曲率的共形度量集。在正Yamabe共形不变量的情况下，证明了该集合在不小于3维的三维情况下是先验有界的，在带脐边界的局部共形平面情况下是先验有界的。

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A priori estimates for negative constant scalar curvature conformal metrics with positive constant boundary mean curvature

On a compact Riemannian manifold with boundary, we study the set of conformal metrics of negative constant scalar curvature in the interior and positive constant mean curvature on the boundary. Working in the case of positive Yamabe conformal invariant, we prove that this set is a priori bounded in the three-dimensional case and in the locally conformally flat with umbilical boundary case in any dimension not less than three.

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来源期刊

Journal of the London Mathematical Society-Second Series 数学-数学

CiteScore

1.90

自引率

0.00%

发文量

186

审稿时长

6-12 weeks

期刊介绍： The Journal of the London Mathematical Society has been publishing leading research in a broad range of mathematical subject areas since 1926. The Journal welcomes papers on subjects of general interest that represent a significant advance in mathematical knowledge, as well as submissions that are deemed to stimulate new interest and research activity.