奇异边界附近完全保角度量的渐近行为

IF 1.5 1区数学 Q1 MATHEMATICS

Advances in Mathematics Pub Date : 2024-10-21 DOI:10.1016/j.aim.2024.109977

Weiming Shen, Yue Wang

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引用次数: 0

摘要

奇异山边问题的边界行为已在足够光滑的边界附近得到广泛研究，而对奇异边界附近解的渐近行为却知之甚少。本文研究了奇异边界附近具有负常标量曲率的奇异 Yamabe 问题解的渐近行为，并推导出不一定保角平坦的背景度量的最优估计。特别是，我们证明了边界上奇异点的解与切锥中的解近似得很好。

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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Asymptotic behavior of complete conformal metric near singular boundary

The boundary behavior of the singular Yamabe problem has been extensively studied near sufficiently smooth boundaries, while less is known about the asymptotic behavior of solutions near singular boundaries. In this paper, we study the asymptotic behaviors of solutions to the singular Yamabe problem with negative constant scalar curvature near singular boundaries and derive the optimal estimates for the background metric which is not necessarily conformally flat. In particular, we prove that the solutions are well approximated by the solutions in tangent cones at singular points on the boundaries.

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来源期刊

Advances in Mathematics 数学-数学

CiteScore

2.80

自引率

5.90%

发文量

497

审稿时长

7.5 months

期刊介绍： Emphasizing contributions that represent significant advances in all areas of pure mathematics, Advances in Mathematics provides research mathematicians with an effective medium for communicating important recent developments in their areas of specialization to colleagues and to scientists in related disciplines.