A note on the Pleijel theorem for $H$-type groups

TL;DR

This paper extends the Pleijel theorem to most $H$-type groups, confirming its validity in a broad class of mathematical structures, with only four exceptions.

Contribution

It proves the Pleijel theorem unconditionally for all but four specific $H$-type groups, advancing the understanding of eigenfunction nodal domains in these groups.

Findings

Pleijel theorem holds unconditionally on most $H$-type groups

Four $H$-type groups are exceptions

Progress in spectral geometry of $H$-type groups

Abstract

We continue the program initiated by [J. \'Ec. Polytech., Math. 12, 1083-1160 (2025)] and show that the Pleijel theorem holds unconditionally on all but four $H$-type groups.