论低规则性约束下陷阱曲面的不存在性

IF 0.5 4区 数学 Q3 MATHEMATICS
Jonathan Luk, Georgios Moschidis
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引用次数: 0

摘要

爱因斯坦场方程解中困顿面的出现与相应的考奇问题在低正则性机制中的良好提出特性密切相关。在本文中,我们研究了当假设 Cauchy 数据的尺度不变大小是有界的时候,在初始超曲面的水平上就已经存在陷落面的问题。我们的主要定理指出,当 Cauchy 数据接近于在 Besov $B^{3/2}{2,1}$ 规范下的闵科夫斯基时空的空间似超曲面(不一定是平面超曲面)上诱导的数据时,最初不会存在陷波曲面。我们还讨论了将上述结果扩展到仅假设 $H^{3/2}$ 小的情况的问题。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
On the non-existence of trapped surfaces under low-regularity bounds
The emergence of trapped surfaces in solutions to the Einstein field equations is intimately tied to the well-posedness properties of the corresponding Cauchy problem in the low regularity regime. In this paper, we study the question of existence of trapped surfaces already at the level of the initial hypersurface when the scale invariant size of the Cauchy data is assumed to be bounded. Our main theorem states that no trapped surfaces can exist initially when the Cauchy data are close to the data induced on a spacelike hypersurface of Minkowski spacetime (not necessarily a flat hyperplane) in the Besov $B^{3/2}{2,1}$ norm. We also discuss the question of extending the above result to the case when merely smallness in $H^{3/2}$ is assumed.
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来源期刊
CiteScore
0.90
自引率
0.00%
发文量
30
审稿时长
>12 weeks
期刊介绍: Publishes high-quality, original papers on all fields of mathematics. To facilitate fruitful interchanges between mathematicians from different regions and specialties, and to effectively disseminate new breakthroughs in mathematics, the journal welcomes well-written submissions from all significant areas of mathematics. The editors are committed to promoting the highest quality of mathematical scholarship.
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