Non-escape of mass for arithmetic quantum limits on hyperbolic $4$-manifolds

TL;DR

This paper advances the understanding of quantum unique ergodicity for Hecke-Maass forms on hyperbolic 4-manifolds by showing that mass does not escape, supporting the conjecture's validity in this setting.

Contribution

It proves the non-escape of mass for quantum limits of Hecke-Maass forms on hyperbolic 4-manifolds, a significant step towards the QUE conjecture in higher dimensions.

Findings

Eliminates the possibility of escape of mass for these forms.

Supports the quantum unique ergodicity conjecture in 4-dimensional hyperbolic spaces.

Provides new techniques for analyzing quantum limits on higher-dimensional manifolds.

Abstract

We make progress on the quantum unique ergodicity (QUE) conjecture for Hecke-Maass forms on a congruence quotient of hyperbolic $4$-space, eliminating the possibility of "escape of mass" for these forms.