共形谐波坐标

IF 0.7 4区 数学 Q2 MATHEMATICS
Matti Lassas, Tony Liimatainen
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引用次数: 0

摘要

我们研究了黎曼流形和洛伦兹流形上的保角谐波坐标,它是作为保角拉普拉斯方程的解的商而构造的坐标。我们证明了共形谐波坐标在一般条件下的存在性,并发现该坐标是谐波坐标的共形类似物。我们证明了共形映射的边界正则性结果。我们证明,如果同时对度量的行列式进行归一化处理,Weyl、Cotton、Bach 和 Fefferman-Graham 阻碍张量是共形谐波坐标中的椭圆算子。我们给出了相应的椭圆正则结果,包括解析情况。我们证明了巴赫平流形和障碍平流形的唯一延续结果,这些流形在某一点附近是保角平的。我们证明了黎曼流形和洛伦兹流形上共形映射的唯一延续结果。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Conformal harmonic coordinates
We study conformal harmonic coordinates on Riemannian and Lorentzian manifolds, which are coordinates constructed as quotients of solutions to the conformal Laplace equation. We show existence of conformal harmonic coordinates under general conditions and find that the coordinates are a conformal analogue of harmonic coordinates. We prove up to boundary regularity results for conformal mappings. We show that Weyl, Cotton, Bach, and Fefferman–Graham obstruction tensors are elliptic operators in conformal harmonic coordinates if one also normalizes the determinant of the metric. We give a corresponding elliptic regularity results, including the analytic case. We prove a unique continuation result for Bach and obstruction flat manifolds, which are conformally flat near a point. We prove unique continuation results for conformal mappings both on Riemannian and Lorentzian manifolds.
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来源期刊
CiteScore
1.60
自引率
0.00%
发文量
4
审稿时长
>12 weeks
期刊介绍: Publishes high-quality papers on subjects related to classical analysis, partial differential equations, algebraic geometry, differential geometry, and topology.
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