MICROLOCAL DECOUPLING INEQUALITIES AND THE DISTANCE PROBLEM ON RIEMANNIAN MANIFOLDS

Alex Iosevich, Bochen Liu, Yakun Xi

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

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.

Original languageEnglish
Pages (from-to)1601-1639
Number of pages39
JournalAmerican Journal of Mathematics
Volume144
Issue number6
DOIs
StatePublished - Dec 2022
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2022 by Johns Hopkins University Press.

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