Microlocal decoupling inequalities and the distance problem on Riemannian manifolds

IF 1.7 1区数学 Q1 MATHEMATICS

American Journal of Mathematics Pub Date : 2019-09-11 DOI:10.1353/ajm.2022.0039

A. Iosevich, Bochen Liu, Yakun Xi

引用次数: 8

Abstract

abstract:We study the generalization of the Falconer distance problem to the Riemannian setting. In particular, we extend the result of Guth--Iosevich--Ou--Wang for the distance set in the plane to general Riemannian surfaces. Key new ingredients include a family of refined microlocal decoupling inequalities, which are related to the work of Beltran--Hickman--Sogge on Wolff-type inequalities, and an analog of Orponen's radial projection lemma which has proved quite useful in recent work on distance sets.

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黎曼流形上的微局部解耦不等式与距离问题

研究了Falconer距离问题在黎曼情况下的推广。特别地，我们将Guth—Iosevich—Ou—Wang关于平面上距离集的结果推广到一般黎曼曲面。关键的新成分包括一系列精细的微局部解耦不等式，这与Beltran- Hickman- Sogge关于wolff型不等式的工作有关，以及Orponen的径向投影引理的模拟，该引理在最近关于距离集的工作中被证明非常有用。

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

American Journal of Mathematics 数学-数学

CiteScore

3.20

自引率

0.00%

发文量

审稿时长

24 months

期刊介绍： The oldest mathematics journal in the Western Hemisphere in continuous publication, the American Journal of Mathematics ranks as one of the most respected and celebrated journals in its field. Published since 1878, the Journal has earned its reputation by presenting pioneering mathematical papers. It does not specialize, but instead publishes articles of broad appeal covering the major areas of contemporary mathematics. The American Journal of Mathematics is used as a basic reference work in academic libraries, both in the United States and abroad.