Higher-dimensional and other-group analogues

Develop methods to generalize the rotational difference-set results for subsets of (Z/p^rZ)^2 to analogous problems in other group settings and in higher dimensions, including extensions of the Section 2 restriction and extension estimates or alternative approaches when those extensions become too complicated.

Background

After proving the main two-dimensional results, the paper identifies broader directions involving analogous problems for other groups and higher-dimensional spaces. The higher-dimensional program would require, as a first step, extending the restriction and extension results developed in Section 2.

The authors explicitly state that they found these higher-dimensional extensions too complicated in the present setting, leaving the development of suitable extensions or alternative methods unresolved.