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 language | English |
|---|---|
| Pages (from-to) | 1601-1639 |
| Number of pages | 39 |
| Journal | American Journal of Mathematics |
| Volume | 144 |
| Issue number | 6 |
| DOIs | |
| State | Published - Dec 2022 |
| Externally published | Yes |
Bibliographical note
Publisher Copyright:© 2022 by Johns Hopkins University Press.
Funding
Manuscript received September 19, 2019. Research of the second author supported in part by the grant CUHK24300915 from the Hong Kong Research Grant Council, and a direct grant of research (4053341) from the Chinese University of Hong Kong; research of the third author supported in part by the AMS-Simons travel grant and NSF China grant No. 12171424. American Journal of Mathematics 144 (2022), 1601–1639. © 2022 by Johns Hopkins University Press.
| Funders | Funder number |
|---|---|
| National Natural Science Foundation of China | 12171424 |
| Research Grants Council, University Grants Committee | 4053341 |
| Chinese University of Hong Kong |