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arXiv · 1909.05171

Microlocal decoupling inequalities and the distance problem on Riemannian manifolds

Alex Iosevich·Bochen Liu·Yakun Xi
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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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Alex Iosevich, Bochen Liu, Yakun Xi. 2019-09-11. Microlocal decoupling inequalities and the distance problem on Riemannian manifolds. https://doi.org/10.1353/ajm.2022.0039

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