Microlocal decoupling inequalities and the distance problem on Riemannian manifolds

Alex Iosevich; Bochen Liu; Yakun Xi

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Microlocal decoupling inequalities and the distance problem on Riemannian manifolds

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arxiv 1909.05171 v2 pith:4WLYLAF4 submitted 2019-09-11 math.CA math.AP

Alex Iosevich , Bochen Liu , Yakun Xi This is my paper · ORCID

classification math.CAmath.AP

keywords distanceinequalitiesriemanniandecouplingmicrolocalproblemworkanalog

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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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