Scattering rigidity for analytic metrics

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-01-30 DOI:10.4310/cjm.2024.v12.n1.a2

Yannick Guedes-Bonthonneau, Colin Guillarmou, Malo Jézéquel

引用次数: 0

Abstract

For analytic negatively curved Riemannian manifolds with analytic strictly convex boundary, we show that the scattering map for the geodesic flow determines the manifold up to isometry. In particular, one recovers both the topology and the metric. More generally our result holds in the analytic category under the no conjugate point and hyperbolic trapped set assumptions.

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分析度量的散射刚性

对于具有解析严格凸边界的解析负弯黎曼流形，我们证明了大地流的散射图决定了流形的等距性。特别是，我们可以同时恢复拓扑和度量。更一般地说，在无共轭点和双曲困集假设下，我们的结果在解析范畴中成立。

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

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.