Work

The fractal uncertainty principle via Dolgopyat’s method in higher dimensions

Year: 2025

Type: article

Abstract: We prove a fractal uncertainty principle with exponent 1 2 dδ + ε, ε > 0, for Ahlfors-David regular subsets of ‫ޒ‬ d with dimension δ which satisfy a suitable "nonorthogonality condition".This generalizes the application of Dolgopyat's method by Dyatlov and Jin (2018) to higher dimensions.As a corollary, we get a quantitative essential spectral gap for the Laplacian on convex cocompact hyperbolic manifolds of arbitrary dimension with Zariski-dense fundamental groups.

Source: Analysis & PDE

DOI: 10.2140/apde.2025.18.1769

Authors: Aidan Backus, James Leng, Zhongkai Tao

Institutions: Brown University, University of California, Los Angeles, University of California, Berkeley

Language: English

Topic: Spectral Theory in Mathematical Physics

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Funder: National Science Foundation

Awards: Graduate Research Fellowship Program (GRFP), G2923451624, G3874738311, Graduate Research Fellowship Program (GRFP), Spectral Theory and Microlocal Analysis